I just won a game -
http://www.whatifsports.com/hd/GameResults/BoxScore.aspx?gid=6023624 - that I was pretty sure I was going to lose because I have the same problem with full-court presses. And this is a *good* full court pressing team, with 5 IQs at A+ and 10 guys at B or better.
I did pretty nearly what jenningss suggested - I play a zone anyway and I tried to slow the game down as much as possible on my end. I also went pretty deep with my bench.
I think (?) it may have helped. I went on a 26 to 11 run in the last 8 minutes of the game to make up the deficit and put it away, and that coincided with the time that I seemed to have the fatigue advantage.
Of course, it's also very possible I just got lucky.