Any number of reasons really, quite often a firewall issue. The easiest solution is to uninstall, restart PC and then reinstall Limewire, it doesn't t ake many minutes and your firewall issues will show up while it's installing as a rule.
I had this exact problem - you need to update your Java installation - Limewire will show you how...sometimes your pc should let you know what updates are available - i.e. Java - it will take a while to install but should be able to connect fine to Limewire afterwards - good luck.
I love the Kazaa Platinum music download service. Verizon said I couldn't download songs...but I have SO many now. Don't listen to Verizon. Start downloading now http://www.kazaa-platinum.com