Are you just not connecting to hosts, or is LW losing it's connection totally?

Do your files start off connecting, then go to 'need more sources'? If that's the problem, sounds like fake files. Search again, vary your search terms (for music, look for artist or album rather than song title) & try the All Types search. Stay away from files with heaps of sources, go for a file with 10 sources or less, or a modem source. Check out the links below for some more info.
Info about fake files
How to find music

For movies, look up a file with Bitzi before download. You'll see other users' opinions of the file. Files with lots of sources but no Bitzi rating are likely to be fakes.
How to use Bitzi

If no files at all are connecting & you're convinced they're not fakes, you could try deleting LW's preferences folder when LW's closed. See points 2 & 3 below for instructions
Fixes for LimeWire