I have the same issue with BTOpenworld. Every five or six days they cycle their servers or something and I get booted. I've been trying to configure ppp to handle this with a clean disconnection and reconnect, but I've not got it working yet.
Sometimes I'll get an IP change and not get booted, but I as I say every six days or so I get kicked.
Very annoying, but then I suppose that I am not meant to be running services on that box either so I wont be complaing to them about it