I've been experiencing similar problems, and have a couple of theories. So far I seem to be having success.

First off, I am running Norton Personal Firewall (which is set to deny all external access), and am on a cablemodem, so I'm behind at least 1, and probably more firewalls. These do not seem to be causing any problem (at least the problem doesn't go away when I turn my firewall off).

Second, and this is pure speculation, it seems to me that the hosts listed in the "AutoConnect Hosts" box may not be responding correctly, producing the eternal "Connecting..." and the connected, but immediately drops off problems.

The one saving grace I found was the discovered hosts section. I was lucky enough to have some discovered hosts added durring one of the short periods that I had a connection. I then selected all the discovered hosts (click on top one, shift-click on bottom), and hit the "Connect" button next to them. This will force LimeWire to try to connect to all of them. This got me up and runnig in a short period of time.

Many hosts still either failed, or dropped off quickly. I believe this to be possibly due to variations in internet traffic, which causes the data packets to take different routes, and take long enough for LimeWire to give up on them. As a result, I would still get wildly varying availability of hosts, and would occasionally still lose all connections. So what I did then was watch the "Connected Hosts" window, pick the hosts that listed the highest numbers of other hosts connected to it (the "Hosts" column) on the far right, and added their ip address and port to the AutoConnect Hosts list. I added about 10 or 15 hosts (unfortunately, there is no cut and paste, so you have to type them in manually--this would be a great thing to add, developers). These hosts will now be polled automatically every time you launch LimeWire.

It can still take a minute or three to start getting good (or any) connections, but once it finds some good hosts that aren't too far away, it works great!! I now am routinely getting 8-32 TB available, 1-4 Billion Files, and 1-4 k hosts!

I hope this works for you guys! Let me know!