Go to LimeWire's menu bar and choose Tools > Advanced Tools. Top left of the window that opens will tell you your status. It will say if you are behind a firewall or not.

Sometimes re-searching the same topic you originally searched will help to get downloads working again. Do not do the identical searches too frequently though, otherwise ultrapeers around you will begin to stop providing results for the searches as they may consider your constant search and result pings as spam. You can vary your search terms if possible.

Keep in mind the network his highly dynamic. People come and go all the time. This includes ultrapeers. So searches can vary after a time. Also persons you were downloading from may have gone offline, or their upload slots have become busy. Unfortunately when people leave the network, their shares are still live in searches for up to about 15-25+ minutes after they have left the network. So sometimes you get search results where some of the persons are no longer available.

If you are concerned about dodgy search results due to being surrounded by bad hosts, open that advanced tools window and remove the first connected ultrapeer (the one that has been connected the longest.) After several minutes try searching again.