Are you sure that you're clicking on the shortcut to LW & not the installer?

If you're clicking on the right icon, maybe one of your security programs is removing LW because it thinks that LW's a threat. Some programs (eg pestpatrol) have been known to do this.
Limewire keeps disappearing! I have to then reinstall! help!!!

Which security programs are you using (AV, antispy/adware etc)?