While players are entitled to play on, if an opponent plays on in an obviously losing position I wont rematch or analyse with them. It's just wasting both players time.
Obviously that depends on the time control, in blitz it's fine for players to play on in much worse positions.
Resigning is not rude, and in fact is polite.
Can't believe I answered, such an overdone topic on the forums.
Which do you find ruder, a player not resigning when they are in a lost position or for them to resign and not let the game finish?