Gnutella clients used to have Automatic re-queries, but the developers had to shut it down and even ban a few clients because they were flooding the network and 'normal' searches and downloads were getting drowned out.
So, the developers have had to come up with other ways, but the ban on automatic queries is still in place.
Sorry--Automatic queries just about killed the network, so the topic is still a touchy one
There is an auto shutdown setting to shut LW down after transfers have finished (it's in the System Tray section of the Options), and LW will try to automatically refind sources for incomplete downloads on start-up. Perhaps that will help a little.