A couple of thoughts;
Is the broadband itself actually disconnecting, or just you from your network? If you are using DHCP, then there is a possibility that there is a 1 week DHCP lease timer set, that renews the DHCP IP address on your device once a week. That could cause an apparant disconnection reconnection, but of your device from the network, rather than the network from the internet.
Alternatively, decent routers (like Draytek) have the ability to have schedules programmed in them for things like timed reboots. Perhaps a weekly reboot programmed?