In short times controls, the rants about people keeping playing unplayable positions is irrelevant imho, as long as the player doesn't cheat (!!!) and keep doing something (stalling-depleting your clock to zero without actually doing something- is actual abuse and on a personal note you end up immediately on my ban list if you do this to me), pretty much everything is ok.
You MUST work on your killing technique instead of begging the other person to give you the victory away.
On longer controls I don't know (It has never happened to me, it is never too late for this).
I have a general guideline for playing on in "ridiculous" positions (as you call them)
You should resign when:
1: You find the win for your opponent, and
2: You have complete confidence in your opponent finding a win.
Example: I've got a bare King against a 1500, who has a Bishop and Knight. Despite my ability to win for his side, I will ask him to demonstrate his technique.
Example 2: I'm a Rook down against a 2000, with little to no active play. Resignation.
Example 3: I'm a Rook down against a 2000, but I have a trap hidden in the next few moves that, if he falls for it, gets me back in the game. I will wait until he avoids the trap to resign.