A postal (or equivalent) game is much harder to come back from than an OTB game. In OTB I won't resign if I have realistic (though unlikely) chances.
Some examples of when I didn't resign a lost OTB position:
1) against another expert I botched the opening and lost a piece for two pawns. I then did everything I could and eventually reached a K+bcgh vs K+B+cg ending with his B stuck behind my bc pawns. I pushed the gh pawns until I could trade them for his g pawn and then moved my K, releasing his B, but allowing me to trade my bc pawns for his c pawn.
2) in a US Open I botched another opening against a C player and ended up in a two pawn down endgame with no real compensation. I declined his draw offer (figuring that he hadn't yet shown why his rating was only C) and outplayed the endgame to win it.
3) in a US Open I had a materially even but positionally zugzwangable game against IM John Donaldson. I mis-analyzed it and thought that it was a draw. When the IM (who was also in the USCF meetings and thus was burning the candle at both ends) proceeded to blow a tempo, the draw actually was there and I drew.
4) in dozens of other games I've played traps, swindles, apparently-ridiculous-but-actually-sound-sacs, etc. to secure either a draw or a win (occasionally the win is due to time pressure errors committed by opponents who didn't have any time pressure before I embarked on complications).
People often say that getting a winning position against me is one thing, but actually winning it is an additional task (unfortunately one that my opponent is up to more often than I'd like). Once all of the plausible attempts have been exhausted I'll finally resign, but I make sure that my opponent earned the win.