Would you ever resign?
Depends on a lot of factors.
i) The rating/strength of my opponent => usually indicates how competent his winning-a-won-game technique is.
ii) His time control situation vs. mine (Blitz vs. slow games? with a increment/delay?)
iii) If this is a tourney, how much of a rest-break do I get before the next game.
iv) The position on the board. This ties closely with i) as the margin of error in terms of "losing" positions can vary from "down a rook pawn" to "down an exchange" to down full pieces. If the margin of error that my opponent has is low enough (with respect to my assessment of his technique). then I'll play on.
For example, If I play a 1600-1800 player who is up an exchange (with no compensation to speak of) or a pawn (probably +1.0 to +1.8 on most computer's eval. scores?), while I am theoretically lost, I certainly don't trust his technique to be accurate enough to close out the game with lethal precision.
Chess games are won by cashing in on mistakes made.... Won games don't automatically win themselves! :)
Based on the above, I'd find no fault for my opponent not resigning for the same reasons.
At competitive play, there's always gamesmanship, ego and attitude and if you are training to play this game in a cool + calm + collected manner, you'll probably leave emotional baggage (irritation, annoyance etc.) at the door before you sit down.
It's just silly to let my opponent get to me using off-the-board tactics or feel arrogant/snarly that he dares defy the Gods of chess and not resign. That's a personality weakness that no amount of chess training will ever correct!
In a losing position, would you ever resign and under what circumstances?
In a totally winning position, where you guarantee a win, do you expect the other person to resign?
If your opponent resigned in a losing position, what would you think of them (i.e. would you appreciate an opponent who has conceded defeat, or would you think of them as a quitter? Would you applaud an opponent who has dragged the game on and on, or would you find them irritating?)?
How many games have you won in a hopelessly lost position?
How many games have you lost in a winning situation?