Wow...that is wierd.
Azureus works through one single port. Open Options and the very first thing on the right side of the screen is "Incoming TCP listen port". Try changing that port to any 4-digit number until you don't get disconnected. You normally will not have to forward the port, but you may have to (depending on your router). That would be your second choice if just changing the port doesn't work.
-Dan The Man
