LimeWire does resume incomplete files, - however if you are downloading a file with multiple locations, the file names and sizes may differ, so not all of those locations will resume the same incomplete file.
As you probably already have noticed, LimeWire will every now and then multiple incomplete files for the same download. That's because results are grouped even if the file isn't exactly the same. If you find the same file someplace else (same size & file name), LimeWire will resume a file without any problems.
I'm about to create a version of LimeWire that will only group results with the same hash. You can download it very soon here:
http://mitglied.tripod.de/mdsgeist/LimeWire.zip
(The previous version also had a problem with the xml docs which I forgot to include in the package.)