If the file comes from a firewalled host and you are firewalled, LW attempts to find another computer to mediate the download (a proxy). Much of the time those they'll be busy.

You can turn off your OSX firewall (System Preferences->Sharing->Firewall) or get your firewall to allow Gnutella/Limewire to go through (System Preferences->Sharing->Firewall->New->Gnutella/Limewire Port 6346). Choosing Force IP in the LimeWire Preferences also helps.

Still, modem connections can be flaky and can disrupt connections often enough to give poor results.

Since search results indicate files that were active once, there are lots of other reasons files can't be downloaded. Still, hope this helps you do what you can.

Cheers