I think was having the same problem ... If I was to start a torrent download after about 3 minutes my connection would stop, and to fix this I would have to power cycle my modem, and unless I throttled the download to almost nothing or i stopped it the connection would shut down again...
I haven't had this problem in a week or two but a few changes that I made that might of helped are :
I started using Azureus (and set up the encryption) was using utorrent and bittorrent before
I started using peerguardian
I ran the WinXP Patch (found here: http://lvllord.de/?lang=en&url=downloads ) - Windows XP limits the number of connections. This patch will change the limit, so you can connect to more peers at a time.
I sill have crappy speeds on my torrent but now atleast I can download them with out losing my connection to the www.
not sure if this is the same exact problem as what you are having, but maybe it will help, or maybe some of the other great minds here can help us both to understand our issues
best of luck...