I think there's a memory leak somewhere. Battles run fine to begin with, but lag more and more as time goes on. It seems to be localized to individual battles though; when I start a new battle, the speed is back to normal.
This issue has been reported before, and Craig believes he has found the cause (http://sinisterdesign.net/forum/index.php?topic=1224.msg48447#msg48447).
Yeah, Flash apparently goes nuts looking for buttons in the object list which seems to grow larger as the fight progresses, even if you might be "destroying" objects as the fight progresses (Perhaps the experience bars created after each attack are new objects not cleaned up?). Once you get a new map the Object list resets so it's all fine.