I recently was given a router, from work, for when I have to work from home.
For the last couple of days my internet connection has been crap, constant "You are not connected to the internet" errors, the mac version of the "cable unplugged" errors you get with Windows networking.
It appears the router, a Linksys BEFSR41 v.4.1 has a bug in the more recent versions of the firmware and disconnects when it attempts to use port forwarding on UDP.
To fix things switch off uPNP and only use the TCP setting in the port forwarding. It you really need to forward UDP (and yes bittorrent works fine without UDP, it's only needed for extra 'off spec' features) then I suggest you get a new router.