Hello mom (great choice of nics!)
Sounds odd. Do you get any error message when it quits? I'm almost thinking that LW is trying to run in Classic mode . . . just a guess.
If you don't mind opening the Console (in your Applications/Utilities folder, it will record more information about what is causing the unexpected quit. You could post the info into a private message or here. With luck that will point to a quick fix.
If not, older versions (ouch!) are available here
http://www3.limewire.com/download/
Regards--stief (thanks for letting us know you'd already done the safe boot/permissions).