Resuming a download can be a tricky thing. LimeWire will not automatically resume for you when you restart. You will need to search for the file you were downloading before. By looking in your library under your incomplete folder, you might see something like this:

Name Type
T-4505182-Kittie - Brackish mp3

You will have to search for this file again using the information in this entry.

From this example, you can see that the complete file size is:
4,505,182 bytes

LW search reports in kilobytes, so it will appear as:
4,505 kb

After the file size comes the name. A dash seperates the file size from the name, so the name of the original file is:
Kittie - Brackish

This is all the information we need:
Name: Kittie - Brackish
Size: 4,505 kb

Now that you have your information, you will search for the file by name once you are well connected to the network. When you find the filename or something close to it, look at its size. If it matches, then select it and click the "Download Any" button. LimeWire should resume from where it left off. I know this is a cumbersome and tedious task, but that's how it is right now. Hopefully, this will change in the future.

And just for the record, I don't like Kittie. This is merely an example. :-)