Try these fixes and lets see if we can keep limewire from quiting, if there is a firewall problem we will check that out, once this problem is fixed...
Try uninstalling all versions of Java from the add/remove programs and then re-install the JRE 5.11 offline version....
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
If that does not help with your problem try deleting your preference folder/s...
Fixes for Limewire when LW isn't operating as it should