I would first try updating the firmware if possible, I haven't had much dealing with these despite being in IT for a living, if you do need the said pre assigned credentials then simply login to your old router to retrieve them, must be something unique to BT though as I have never come across it!

Personally I would be looking at the Xbox/location first, you say other devices work but do they work in the same room as the console?

It may not be the connection dropping out every 3 to 4 days, I.E the wireless/LAN connection but you may be loseing your WAN connection and a reboot resolves this.

Next time it happens try pinging the router itself, if you can see it then it's NOT a router problem.

Martin