Also started experiencing the slowdown today (Brain Party 0.5.91-2). I looked at ".brainparty" in my home directory and it had some 2.6 million lines, a bit on the large side isn't it?
How large should ".brainparty" be?

It looked like it was keeping the history of all games (the scores) but repeating it over and over.

I tried trimming it down to no avail: still slow-down. Threw it out and Brain Party runs fine again (like starting from a fresh install, i.e. no history of previous games).

This game is great fun, so I hope you're able to sort out the slow-down glitch!