That behaviour sounds very odd! It's almost as though you have corrupt preferences or something. If your downlds were going to lose their progress, then normally if there was an issue it would be reset to zero. And that only happens if your comp crashed or you didn't close LW properly before you shutdown the comp. Try deleting your LW Preferences folder whilst LW is closed; instructions here: Fixes for Limewire

The issue couldn't have something to do with the office backup system could it? Do you log into the exact same terminal or comp everyday do you?