Highlight the download you want to move and click on launch. It should send it to the main library for iTunes and you can find it there. This works for incomplete downloads as well if you want to preview the song before the download is finished.

I get this problem once in awhile and usually if I log out of Limewire and right back on it is ok.

My problem seemed to be caused by the fact that I moved the Shared folder in my directory to another location. Once i moved it back to the Limewire default and kept the Application in Applications all was well again.

Let me know if this helps