I don't know the belkin very well, but I presume you've not got a connection timeout set, or you have made sure if there is an 'always on' connection tickbox, that it's ticked?
The only other thing I can think of is if it's set up for PPPoE rather than PPPoA. If not, it may even be a faulty router... occasionally happens I guess, although amazingly for the number of routers sold in the world there are surprisingly few that turn out to be faulty! (off topic I know).
Bit of a weird one though... have a look to see if there's any kind of log in the router, that'll maybe tell you why you can't maintain a connection.
Good luck!