Thanks guys! That totally was the problem! Well, not totally, but I've been able to solve the problem.

I disabled the Ultrapeer capability and Limewire ran great for several hours while I used the computer. I then left for about two hours or so, came back, and my screen saver had filled the screen but was frozen. A hard restart was the only recourse. I remember reading stuff about OS X having various issues with sleep and screen savers so I went and turned those off. Limewire's been running great since! Thanks for the help!

Roger