Is it disconnecting after your computer goes into stand-by or mode hibernation mode? You may need to adjust your settings.
Go to your Control Panel > Performance and Maintenance > Power Options, and try setting them to never and see if it helps. To narrow it down just do one at a time.
Sample image:
Power Option Properties
If that doesn't help, try deleting LW's preference folder with LW completely shut down. Instructions in this thread points 2 & 3(check both locations):
Fixes for Limewire. This will reset all your option settings, so make a note of them first.