I think your opponent might be hoping for stalemate, or more likely, just likes to say "SPARTA!" ☺
In this situation I would prefer to sacrifice the queen and then checkmate by promoting all the pawns to knights and/or bishops (unless it was a blitz game).
I'd rather not try to do the knight + bishop mate, but it'd be interesting to actually do the 2 bishops mate for once.
I meant promote ALL the pawns to minor pieces, like in this game:
http://www.chessgames.com/perl/chessgame?gid=1497429
Other people suggested the idea too on another thread, but I forget the name.
Waiting for the stalemate probably !
I would resign in such a situation but against a Knight and a Bishop, I would let my opponent prove that he knows how to checkmate me : )
That said, your opponent has probably not read my blog post about how to checkmate with a Queen and a King:
http://chesstrainerapp.blogspot.com/2013/12/how-to-checkmate-with-king-and-queen.html
Smooth 15 month necro.
I'll go back in time to figure out which game I was speaking of and then ask them. I'll then lend them my TARDIS so they can come to their future to read your blog. Perhaps I already did. It is hard to keep track.
I meant promote ALL the pawns to minor pieces, like in this game:
http://www.chessgames.com/perl/chessgame?gid=1497429
Other people suggested the idea too on another thread, but I forget the name.
Rybka? 
Some people like to play all the way to mate. It's their right. Why do you think you have any right to be annoyed?
Such players have the right to play to mate. And their opponent has the right to be annoyed. I have the right to pick my nose in public, but it is still bad manners.
When a player who is both old enough and good enough to know better does not resign with a lone king against many other pieces, I have the right to choose not to checkmate for several hundred moves.
Sometimes in blitz if you're low on time, and especially if you have an increment, you can just limit the king repeatedly with the queen until they have only one row to go. It's not accurate but you don't have to think much either.
Sometimes in blitz...
Blitz is different. I have no problem with someone not resigning until mate. My comment refers to correspondence games with at least 1 day to move. Playing on in those games is absurd.
Yep, 15 months later.
Why do people keep going when it's a king + queen vs. queen? I know there is a chance of a stalemate, but sometimes they keep going all of the way to checkmate. Then there are those times where they keep playing until the side with the queen has a mate in 1. The worst is when they make their last move and then resign faster than you can move the queen! I don't understand it. I'd understand it at low rating, like 600.
Yes, I'm a little annoyed. Here is the final position from my last game (following 13 turns of K+Q vs. K):
Promoting my a-pawn might have been faster.
It was sort of funny since they dramatized it by saying they're going to fall on their sword and typed "SPARTA!"