He has two queens. I have one. Is it proper chess etiquette to check him non stop just to avoid losing? I am losing a game. My only option is to check my opponent non stop. I have no chance to checkmate him. I am only hoping to force a draw. Is this proper chess etiquette?
What you are describing is Perpetual Check: http://en.wikipedia.org/wiki/Perpetual_check

It is covered in the rules of chess and the result of such a game is a draw. It is up to your opponent to try and avoid this situation if he thinks he can win. Conversely, if you might lose you should try to get into some kind of draw situation to avoid a loss.

Anecdote: A queen vs. queen, knight, and bishop did the same thing at the club quick tournament last night.