Its a bummer some of you are still experiencing connection problems. I suffered from this until about 6 days ago. Now it stays connected most of the time (not always, though).

I have played many games to make this work, but it appears that the most important thing was to make sure that every host in the autoconnect list is up. EVERY host. I would think that limewire would just skip a down host, but this does not appear to be the case for me. At the very least the behavior is non-deterministic.
Right now I have connect4.bearshare.net, connect1-3.gnutellanet.com and gnutella-again.hostscache.com in the list.
I also select "prefer autoconnect hosts". I have very little faith in discovered hosts and clear out the gnutella.net file every time I restart. Similarly, if I see a bunch of hosts with the status of "connecting..." for longer than a minute (less when I feel impatient), I remove them. This brings in a set of new hosts for limewire to try. Sometimes this is just a cat-and-mouse game, but at least I see limewire working.
Occasionally, I will check out www.gnufrog.com, and add one of those machines under "Connected Hosts" (Check the port, its not always 6346)

This has been working for the last 6 days, meaning that I am able to download and upload, and usually have between 1000 and 3000 hosts on my connections tab. During busy times of the day (10am - 7pm ET), the number of hosts can fluctuate wildly.

I like gnutella networking a lot, but I fear the problems we are all experiencing are related to an inherent scalability problem with the current design. I won't bore you with the details, but, mathematically, the current design is far less than ideal (Trust me, I am being extremely kind). I hope that the wizards that created it are working on the next generation. BTW, I am not talking about LimeWire here, I am talking about whats underneath.