Frankly, I think both you and your opponents who asked you to resign were being rude.
It's unreasonable to demand a resignation.
But I think its even worse to continue to play on when you have no conceivable chance of even drawing.
I think a fair compromise is, if you wish to ask someone to resign you should also post irrefutable analysis that leads to mate, a pawn promotion or some other unlosable position.
Okay, so I have recently played several games where I am in a fairly lost position but sometimes I like to play to learn or just to see if my opponent knows the endgame.
In some of these games my opponents have either hinted that I should resign or flat out asked me to resign.
I don't know if it is just my rebellious nature or not, but asking me to resign is sure to make the game get drawn out longer by me making them checkmate me.
This may be in part to the first chess book I ever got by Silman which gave info on openings, middle game, end game and other factors. One of those other factors said that you never have to resign. You can make your opponent beat you in the openings, middle game and end game.
There have been times where I just didn't want to continue when I know I've lost, but isn't it some breach of etiquette to tell your opponent to resign?
Sure, it might be considered rude and some may assume that you think you can still win if you don't resign. But I've played enough games to see that just because someone can win the opening and middle game doesn't mean they can't blunder or that they know their endgame. It may be unlikely and don't tell me that high rated players don't make mistakes because I've played in several USCF rated tournaments where I beat players in the 1800+ range because they made mistakes.
I'm no where near the best, but don't tell me when to resign, or else I probably wont.