No one ever won anything by resigning. Even GMs missed mate in two
When should you resign?
In losing endgames you should play for checkmate because your opponent may stalemate you. In the 1400 Level you should resign because your opponent knows how to convert the advantage.

Resignation isn't really a courtesy to your opponent -- rather, most players like executing the winning game -- it's a courtesy to yourself.
If you believe continuing to play would be a waste of your time, resign.
If you play to win and won't win, resign.
If you play for fun and won't have fun, resign.
If for any reason your time would be better spent elsewhere, resign.

> Even GMs missed mate in two
And Kasparov resigned a drawn endgame against Deep Blue.
But the hard part is finding that M2 or draw; just pushing pieces around isn't an different than resigning if you don't find that line.

Here's what you should do.
1)Get into a completely lost position
2)Wait until one minute before your time runs out
3)Resign
In OTB chess Ive had a few opponents who got up and walked away and never came back when they were in a losing position.

When the piper is gone and the soup is cold on your table,
and if the black crow flies to find a new destination --
That is the sign.

Don't resign on any terms other than your own. Don't feel bad or awkward playing every one of your games to the bitter end even when you know its hopeless. It is your choice too do otherwise.
IM Silman has excellent advice on this topic. He's part of the chess.com community, maybe he will share his thoughts?
A bunch of us witnessed this exact mindset a couple years ago at a tournament in Reno. King vs. King and rook endgame. The guy would not resign. He sat there for 5-6 minutes a move, basically long enough to make the time control and his opponent wait. Obviously it is right to play on, but what was wrong about it was that his opponent was in a tie for first, and im sure would have appreciated some rest before the last round. So after he checkmates his opponent, his opponent goes into the hallway and brags to some friends about how he made him wait so he couldnt unwind before the last round.
I think that is when its wrong to "play on til the end" It also shows a complete lack of respect for your opponent and the game.
The discourtesy was taking 5 minutes a move, not refusing to resign.
If an obviously winning player took an excessive amount of time that would also be discourteous (although not really a problem since the opponent could resign).
No one minds playing an obviously winning position. The more winning it is, the faster it ends. But playing 5 minutes a move is different.
Keep in mind that a 1-1/2 pawn material advantage (engine evaluation) is generally considered a "winning advantage," in most positions. When you have that advantage, tell yourself -- "I should win this game, if I don't get checkmated out of the blue."
Um, wouldn't you have to be playing with a chess engine on in order to know when you have +1.5 engine evaluation?