Originally posted by atticus2
It is widely regarded as a discourtesy, even an insult, to play on beyond the point where, by reasonable means (ie moves) from the opponent in question, you will lose. The relative strength of one's opponent is an important factor in making a judgment on when that point has been reached.
I'd agree with that. It is discourteous to play on in a lost position.
However, so is asking your opponent to resign - you are throwing his judgement into question.
Depending on the day, I might play on to the bitter end and add the opponent to my censor list, or I might reply that I had intended to play on for a few more moves, and still intend to do so.
A third reply might be that the mobility of your pieces more than makes up for the material, so he is free resign if he wants the game to end.
In an over-the-board tournament, my opponent offered a draw quite early. I could not see a good reason, but he was a stronger player, so I accepted. He told me afterwards that his car was badly parked, and he needed to move it. I always wondered would would have happened if I had played on ...