How do you decide when to resign? ...
If someone is online and playing quickly, I'll generally let them finish off a mate, but otherwise I'll resign when I'm pretty sure I have no chance to save the game. When I play live chess, I'll play it out, but why prolong the agony in a game that's already been going on for six weeks?
+1 precisely it; why prolong a game where both players know the result? Obviously, many factors should be considered when deciding resignation. The most intuitive is the rating of the players; stronger players will tend to resign earlier because the margin for error is less in those games and both sides are well versed enough to identify winning/drawn/losing endgames faster than the weaker chess player. However, time control also plays a factor - again due to "why prolong the inevitable?" If it is a bullet game of 1 minute then it is reasonable to almost never resign, but OTB or "daily" correspondence games it feels harder to justify why the players waste their, and everyone else's time (at least my view on it).
However, the majority of chess players are not GMs and surprisingly: the majority of chess players aren't even considered "strong" by many (although "strong" is subjective from person to person). Statistically, plus or minus 8.00 evaluation is when most players resign! Although I am sure that is greatly skewed by players who "never resign" - but the "average" chess player is only around 1000 rating, so it makes sense to a degree because at this level the opponent is prone to mistakes (average rating varies a bit based on rating system used and pool of players competing, but the "average" is usually between 1000 to 1200 rating [true on chess.com as well]).
In short, I expect resignation earlier by players who can better evaluate the position on the board. With this said, I am a determined person and I certainly don't want to lose - however, I resign when I don't see myself succeeding in that position. That is the key: different players have different feelings on how realistic their analysis of the position is (some don't resign because they don't see just how bad it really is at the moment).
Interestingly, I often resign or not based on what technique I see the other player playing. Let us assume a hypothetical pawn endgame where one side is dominating and the losing side can only hope to win by a mouse-slip (or many) or disconnection. In this case, I would almost always resign if I was the losing side (as would most players). However, before I mindlessly click that "resign button" I observe their converting technique. If they are playing the moves I predict, or simply going after another efficient checkmate, then I resign out of humbleness and respect. However, if I see the opponent aimlessly moving pieces around or simply pushing pawns (you would be surprised how many players do this), then I continue the game. Why? Am I spiteful, or something? No, on the contrary. Remember how I said the key was how one "feels" about their winning chances (or lack thereof), if they seem to know what they are doing - I have no chance of winning and I resign. However, if I observe that they are not playing the ending efficiently, then I "feel" that I have a better chance of them messing up. In this case, I play a strong defense and try to set up potential stalemate tricks. With any other player I wouldn't bother wasting our time, but if I think they don't know what they are doing: I "feel" like I can cut my losses by playing on (usually snagging a draw, but sometimes even a win, but these results are ALWAYS against playing who doesn't know what they are doing).
How do you decide when to resign? I've had some weird experiences lately in daily chess. I was playing in a tournament where one of my opponents was rated 400 points above me. They resigned the first game earlier than I expected - when I had Fritz analyze the game, it gave me a +2.7 advantage, which as a 1400-rated player, I am perfectly capable of messing up. As an 1800 player, they probably wouldn't and gave me the benefit of the doubt.
In the second game - they weren't having a good week apparently - they resigned with a +1.1 advantage! To be fair, there was only one move that would save them from a forced mate, and it wasn't particularly obvious, but I was still startled.
(I don't have room to talk - in another game, I offered a draw only to find out Fritz thought I had a +2.6 edge.)
On the other hand, I'm in a 3-day game where I'm up a queen, a rook and three pawns. My opponent is playing a move about every 60 hours with a king and four pawns and has gone on vacation multiple times during the game. We've been going for two months, and this is only the first of our two-game series.
If someone is online and playing quickly, I'll generally let them finish off a mate, but otherwise I'll resign when I'm pretty sure I have no chance to save the game. When I play live chess, I'll play it out, but why prolong the agony in a game that's already been going on for six weeks?