There's nothing wrong with the resume on LimeWire. If the file is online, search for it again and it will come up with the incomplete icon (a ripped piece of paper) then just click to download it again.

This thread was started three years ago, guys. It's no longer a problem.
If LimeWire can't find sources for your incomplete downloads even when you've searched for more sources (and by this I mean actually searching, not just clicking "find more sources") then there are probably no hosts for the file/s online, which means that even the Java gurus on the LW team can't do anything about it!

Just remember that whenever you search for a file in the first place, try to download the one with the most sources if possible.