Stalemate is only one type of draw that is possible in chess. There are other ways, some of which are specifically designed for the situation in which you currently find yourself. But they require additional effort on your part. Look up the Threefold Repetition and 50-move draw rules - in particular, how to go about claiming them on this site (many people mistakenly believe that these are automatic; they are not).
Neither player can win but can't force stalemate
Looking at your active games, it looks like they've all still got life in them. You can try for a three-fold repetition or the fifty-move rule. You're always welcome to offer a draw as well. But, you might be surprised how a seemingly drawish position can come to life.

Excellent. Thanks guys. mjh, you may well be right that the game in question still has life. Not a lot it seems. One thing is for sure, I seem to have lots of time to look into each of your suggestions.
: )

Just remember, to get the 3-fold repetition draw, you have to click the draw button, it is not done automatically.
Once you finish your game, I suggest you toss it in an engine. I think there might be something worth seeing in your endgame. At least if the game you are playing against d0nkeyw0rk is the one.
What's the deal with a game that cannot be won by either side (as long as I just keep pushing my bishop back and forth) but can't force a stalemate? It's the deciding game in a tournament and the guy has been taking forever in the firt place. Somehow I don't expect him to accept the draw.