When I use Azureus and my G5 goes to standby my wireless router will loose the internet connection until I restore factory settings and reimport my backup.
It's doing the same on mine to. I've tried Limewire, Bearshare,Frostwire, and 2 different torrent programs. All with the same results. I heard it was a problem with the firewalls but I disabled them and it still would drop.
It's your router. It can't handle all the connections. You probably have a netgear or dlink budget router. Get a linksys and your problems should be solved. If not, return it.
Wireless? Try wired and see if it works. I had something similar happen. Just thought my POS router was giving out, but now I wonder if it might have something to do with the new tcp stack in Vista causing the router chipsets to puke. It only did it to me with torrents, but considering the nature of p2p traffic vs most other that might make sense.