Grr I hate these BT routers. Do you mean the 2100?
If ISP's detect alot of activity on P2P ports sometimes they will force a disconnection on the line in question so you loose queuing and free up bandwidth for people in your area, since on your ADSL connection you'll be effecting everyone else's contention ratio [in the UK out contention SUCKS]. Try it without your P2P running, just browsing etc and try in the morning and see if it is still working. If so *ding* there's your issue. If not, could be a faulty router/modem.
MikeHP