Factor "Y" mentioned above: Yes, the mental cost to future games of continuing to play would have to be considered in relation to the question "why resign?" That mental cost might be statistically lower than people think. Studies of expertise show that experts are often poor judges of the limits of their own expertise; an expert chess player may be an expert at calculating chess moves but might not be an expert at calculating the statistical significance of the mental costs of making chess moves.
Why are chess players quitters?
A good analogy is found in Moneyball: The Art of Winning an Unfair Game describing how baseball experts at the highest levels were deeply flawed about their own expertise in making baseball-related judgments.
Your response ignores the race analogy. If some runners have already crossed the finish line and won the race, but you're way back still running the race, you can't score, you can't make a threat, you can't do anything to affect the outcome. The outcome of the race is actually already officially decided no matter whether the rest of the runners resign or keep going, unlike in chess where it's still not an official outcome no matter how lost the position until the person resigns. So Olympic runners should just stop running and walk out?
For a runner, it's not just the victory that counts. The placing and the time might also be important. Only if all other competitors have already finished and the last runner has no chance of finishing in a reasonable time, the comparison with chess fits better. But in this situation many runners would also just quit.

if my position is pretty much helpless, i.e I'm pretty much stringing out the game in the hope of a freak mistake, then my philosophy is have the good grace to admit defeat. Do you not feel by the end of the game there is normally a sense of honour towards the player that has bested you, and to have the good grace to resign is the most fitting way to end the game? Rather than an undignified hide and seek that often occurs. Obviously, if I feel there is a chance that they'll get me in check mate relatively quickly without the game descending into farce, then I continue until they get their moment of glory. Chess is not a sport, the etiquette is different.

"Furthermore, I'd like to note that these types of questions seldom come from high-rated players, which should tell you something about their nature."
Are you familiar with groupthink? Or the global financial crisis? Lots of experts can sometimes all do something unthinkingly just because that's what everyone else is doing. I can list endless examples of this. Actually this idea that we shouldn't question "experts" is the single biggest problem in the world.
I think the culture should change and games should be played out longer -- at least until the endgame. Even top players will sometimes make mistakes. Why give up and quit if you still have a 5% chance of winning or drawing through less than perfect play by your opponent or some other occurrance?
As expected, you completely failed to address the rest of my comment, which is where the meat of my argument was. You are not interested in serious discussion, and most likely you are not even being sincere.
I implore you to read the rest of that comment I posted and actually argue its points, rather than the aside I threw in at the beginning of the post.

Here, I'll even help you by posting the rest of the comment right here:
"With that out of the way, I'd like to point something out that everyone here seems to have missed. In virtually all physical sports, people watch not only for the result, but also for the physicality of the players. I can attest to this, as I've recently explored American football, and my primary reason for watching is just to see the crazy athletics at play.
In chess, there are indeed many mental gymnastics which make the "sport" fascinating to watch. However, when a player is "busted" (where most serious players resign), there is nothing of substance left to watch. Likewise, there is nothing of substance left to play. Even if the player can miraculously win, there is nothing interesting here; only some massive mistake by the opponent or another form of oversight (maybe clock management).
In a race, one gets the sense of a runner overcoming all odds to come out on top by expressing true physicality; i.e. their physical genius. In fact, the only way you'd come back from such a deficit is if you run faster than you've ever ran before. In chess, if a player draws a Q & K vs K ending, it's just a disappointment for all involved. Nothing exciting, nothing to be learned, and 99.99% of the time nothing to be gained. Conversely, you can save time and play another game or just rest your head by resigning."

That actually happens in football. I've seen games with multiple red cards where one team is playing 11 against 9, and the team with 11 runs up the score. The team with 9 players ("pieces") left doesn't then resign their hopeless position.
They do. Propriety and the genuine threat of sanctions levied by governing bodies prevents them from actually stepping off the pitch, but they effectively do and if you can't see that then I would suggest you're a rather unobservant sports watcher.
Hell, to use the English league as an example, teams like Aston Villa and Swansea City have effectively resigned the remainder of the season, the latter after securing survival with an excellent display against Chelsea and the former because they're dog*****
This seems to be a key point that a poster makes above: "etiquette" -- a certain cultural ethos that exists in the chess community. It's interesting that this etiquette favors the stronger players over the weaker ones (a cultural pressure to resign favors stronger players over weaker players -- both in terms of an unequal background psychological pressure and in terms of the possibility of resigning a game that could've been drawn or won).

it's a bit like in formula1 where the faster cars are at the start of the grid so Mercedes wins every race.
Let's ignore high-level chess for a moment. And this is a slightly different angle. At my level I think people resign too soon. They ought to play out more games even if they are supposedly "clearly" losing. This is anecdotal evidence, but in my experience, I've kept playing games that I've been pressured to resign and ended up on occasion with a stalemate or perpetual check or other draw, or even a win. I keep learning in such situations even if I was in a losing position. I've had people claim that my draw or win was somehow "BS" because I should've resigned a clearly losing position.
I think the so-called "etiquette" and ideas of "respect" ought to be open for debate and not accepted as some unquestionable theology.

The problem is that you seem to only care about results, rather than the game itself. For an athlete to win from a totally losing situation, it would require incredible athletics and genius. An American football team coming back from a 30 point defecit would require brilliant play (possible some spectacular catch). A sprinter coming back from a 10 yard defecit would require tremendous speed (probably the fastest speed of their career). These things mean that there is a lot left to watch in "losing positions" in other games, and moreover, a lot left to play.
In chess, the act of moving pieces is not interesting. It's the act of actually thinking about positional complexities that makes it an interesting game. In totally lost positions, there is nothing left to think about. As I've already said in a previous comment, if a player draws a Q & K v K position, it would be a disappointment for all involved.
I've played Q & K v K position and my heart was racing how exciting it was -- with both players having only a second or two of time left, as I make my moves to maximize the chances of -- and sometimes achieve -- a stalemate.
Obviously with infinite time, there are good reasons to resign the losing position in Q & K v K. But that's a rare situation. I'm talking about the situation in which most games are resigned. And ignoring high-level chess for a moment, I think too many "lost" positions are resigned too soon. Or put another way, I think a small but significant number of such resigned games would have had a different outcome had they been played to conclusion.

Short answer: resigning is not quitting. Resigning is an act of intelligence, quitting is an act of weakness.
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A professor I knew used to say that timed sports are designed for the entertainment of the working classes. Workers have their "fun" restricted so that they can work the next day. They have paid their tickets to be entertained for a certain amount of time and they would get upset if their entertainment is cut short: the show must go on.
This works well for the television, too. If you know that the football/soccer game is going to be 90' you know how much adverstising you can sell and you can program the next shows. If the match stopped before that time, the advertiser wouldn't be happy. Everybody must play on, more commercial are coming.
Therefore, the ethos of staying after you've lost is related to economics, not to the quality of your character.
The case of long distance runners might be different. However, I can't help but wonder how many would quit if people weren't looking.
Another interpretation is that chess is a game of war. Resigning is like surrendering. If you've lost the battle, you must stop the suffering.
Your response ignores the race analogy. If some runners have already crossed the finish line and won the race, but you're way back still running the race, you can't score, you can't make a threat, you can't do anything to affect the outcome. The outcome of the race is actually already officially decided no matter whether the rest of the runners resign or keep going, unlike in chess where it's still not an official outcome no matter how lost the position until the person resigns. So Olympic runners should just stop running and walk out?
Yes

Pobokov73 wrote: "if my position is pretty much helpless, i.e I'm pretty much stringing out the game in the hope of a freak mistake, then my philosophy is have the good grace to admit defeat."
Agreed, with the one exception of situations where the materially and/or positionally superior player is short of time. If their clock is so low that there's a chance they could blunder a won position away, or simply just not have sufficient time to execute a mating attack, I'd play on in hope of a draw.
Edit: "play on in hope of a draw" if I was literally down to my king. Otherwise it'd be a win on time. Sorry, was thinking of a game where I had K+Q vs my opponent's K+P but less than a minute on my clock, and declined an opportunity to take his pawn in favour of a mating attack but ran out of time and actually lost the game...

I understand, from this I imagine you play at a much higher level than me, I've never played in a competition. From my point of view, the game can be so beautiful that for it to get scrappy at the end lessens my appreciation of what has occurred during the game. Obviously, I don't like to lose but I'd rather those I play know that I appreciate how they have won and aknowledge they were better during the game and end it well, than for four or five days worth of thought to turn into a undignified game of hide and seek at the end. I know it is my responsibility to win the game when I am top, but sometimes somebody just prolonging a losing position in the hope of a draw seems to go against my ideas of how chess should be played. We have to deal with enough bad faith in life - chess is my escape from all life's crap. Sorry to talk rubbish guys, recently re-descovred the game afters years away, so tend to be a bit pretentious about it all. ;)

When I began to play chess, long time ago, someone taught me that when I figured that I was in a lost position, I should resign, as a way of showing respect to the higher level player and also not to insult him with some feeling that "maybe he/she will blunder". I have learned that in chess, this is a compliment, a gesture of respect to your better rated opponent. I think that is ok.
Yes: "A very much won position of a similar complex nature to an equalish position would produce far fewer blunders/major mistakes from the master than the equal one because the priorities of the game have changed. "
That would have to be factored in.