I am playing a game against a stronger opponent, and I am winning.  I have three passed pawns, two of which are advancing against my opponent's one remaining piece (a rook), his king is cut off by one of my rooks, my other rook is supporting the advancing pawns, and my opponent is 8 points in the hole.  All in all, the game is lost for him.  I asked him to resign because it became obvious that, by moving as little as possible, he was stalling the game (likely hoping I will time out).  At first he didn't respond, so I played on for another month.  I recently asked him to resign again.  This time I pointed out all that I have told you and added that "even a beginner would find it extremely hard to throw this position".  He responded by saying it was his right to play until the end, and asked me to stop with all of the useless talk.

Here is where my problem is.  Do we, as chess players, have a right to play on?  I know it is "legal" in chess to do so, but I thought that basic chess etiquette was to resign.  Any other thoughts?

Asking an opponent to resign when a position is lost doesn't seem impolite to me.  If you wait until the position is lost, and it is clear your opponent isn't resigning.

Agree with you totally. It would be really boring to be the opponent, but (s)he is probably waiting for a mistake at your side...