You can right-click any of your downloads and choose Try again, or use the Try again hyperlink to the far right.

But searching for fresh results has always been the best way to find more sources for the downloads that have stopped. The hope is that someone else also has the identical file. If not you need to be patient and the file may download at a later time or day.

There are what's known as fake files out on the network. Some of the anti-file-sharing companies spam these into search results. Some are bad files, some are files that can never be downloaded I guess because their upload slots are closed.

Was LimeWire blocked from the firewall before you started having this problem? Firewall issues usually only affect uploads but strong firewall set-ups might also affect connecting and maintaining connection with some hosts.