The best way round this is to kill the download and reselect it from the search results list. This will force Limwire to ask for the file again and if some of the file has already downloaded it can resume. If that doesn't work, you can try repeating the search and doing the same (kill and reselect) if the file appears on another host. If you select the file from another host, it must be exactly the same version (check name and size). To make sure you can compare the hash numbers by right clicking [Windows] or command clicking [Mac] on the file and selecting Bitzi Web lookup, though this is a bit tedious to do.

Sometimes this won't work, though, especially if it's a highly demanded file.