I think that this game is not a good example for "not resigning", because it was a live game and anything can happen there, especially at blitz and bullet.
And the game wasn't totally and utterly lost, at least not for an average players.
THIS is why people don't resign
Sort:
Sorry, it was the best I could do. That's why I asked people to post their games!
But to be honest, time was not really a factor in the above game.
I think that game posted by "get_lost" here is a better example:
http://www.chess.com/forum/view/community/vacation-adjudication-in-a-winning-position?page=2
The shorter the time control and the time left, the weaker the players, and the smaller the disadvantage on the board, the more reasonable it can be to play on and not resign.
The longer the time control, the stronger the players, and the bigger the disadvantage on the board, the more sense does it make to resign a losing game because the rest has become obvious and uninteresting for both.
So one should not say "always resign early!" when there is good reason to assume that the opponent's technique and remaining time may not be sufficient to make the rest of the game an obvious and uninteresting task.
And one should not say "never resign!" when, in view of the opponents strength and remaining time, the rest of the game will be easy enough so that, for example, both you and your opponent would be able to finish it off without problems worth mentioning.
Play on while there is something interesting to play for, resign when there isn't. 
Here's my example. The thing is, here I was playing against my chess computer, which is obviously quite a bit different than playing against a human being, but I think it demonstrates the benefits of hanging on through a terrible position sometimes.
ilmago wrote:
... one should not say "always resign early!" when there is good reason to assume that the opponent's technique and remaining time may not be sufficient to make the rest of the game an obvious and uninteresting task.
And one should not say "never resign!" when, in view of the opponents strength and remaining time, the rest of the game will be easy enough so that, for example, both you and your opponent would be able to finish it off without problems worth mentioning.
Play on while there is something interesting to play for, resign when there isn't.
Right on!
Here's another example, in which I saved a game from a spectacular fiasco against my computer.
quixote88pianist wrote:
Here's my example. The thing is, here I was playing against my chess computer, which is obviously quite a bit different than playing against a human being, but I think it demonstrates the benefits of hanging on through a terrible position sometimes.
I guess... but the way computers make mistakes (intentionally or otherwise) is radically different from humans. I've played against a "mellowed down" computer that tried to approximate my level of play - sometimes it made an absolutely ridiculous mistake that a human would never do. Like this one, where Shredder decided to go Bongcloud on me:
Wow! That was shocking. I think that's rare for a computer to do something like that; I've never seen it. In a way, doesn't that make it a bit more human-like? Because computers just don't make moves that allow mate-in-1, especially from a winning position like that! But people do occasionally.
quixote88pianist wrote:
In a way, doesn't that make it a bit more human-like? Because computers just don't make moves that allow mate-in-1, especially from a winning position like that! But people do occasionally.
It's supposedly programmed to be more human-like in that at random moves, it chooses sub-optimal or even blundering moves. That's just fine, but I would expect blunders to stem from following a straightforward plan while overlooking something obvious. In the above case, however, I can't understand why anyone would make a move like 19. Ke2 - it simply has no motivation.
But we digress...
A good topic You have here... Unfortunately I cannot remember any recent game when this happened but I am sure I've had some.
This is a game i played live last night after a couple of drinks and i think it fits perfectly in this thread. After a mistake i was left with a knight against a bishop and a rook. My opponent was lower rated than me and i figured i could try to confuse him with some fancy knight tricks before i resign. After a few moves i forked his rook with his king and eventually i saw a stalemate opportunity and he fell for it thinking i was offering him my knight for free!
Good one, tsilis!
Here's a game I chanced upon while browsing the forums, i.e. I'm not either player:
That's a good one Tsilis! Congratulations.
I think a lot of it depends on your confidence that you can pull something out of the bag. I've had matches on here and offline in which I was in a worse position but felt I still had enough material or the position to get a result. In some cases I've managed to pull it off, in other cases I admit I have probably gone a few moves beyond the realms of courtesy but have still resigned rather than forcing my opponent to play it out and in some cases I've felt I could swindle my opponent out of a win and it's actually enjoyable to be shown I was wrong and enjoy the technique they displayed in forcing the win.
[DELETED]
Everybody's always whining about why won't so-and-so resign when he's down on material. The reason is that your opponent has a low rating, which usually means that you also have a low rating, which means that you may still blunder horribly. So I had an idea: make a thread where people can post games where this has happened (going from a clearly losing position to a draw or even victory), so that later on, when the umpteenth why-won't-they-resign thread appears, you can just post a link to this thread. If you have such games, post them here!
I'll start. I still haven't gotten the hang of live games: I build a strong position, get distracted, and then blunder a piece or even two, as in the following example. But when your opponent's rating is only in the 1600's, that doesn't mean you have to give up!