There's an odd fairly rare problem I've been seeing with two plusnet broadband accounts. I've tried raising a ticket previously and been told it's a router problem, which may be partly true, I don't know.
The problem is that sometimes the router fails to establish a PPP connection. The way this shows up varies. When I was using a SAR110 I would suddenly lose internet access, but the action of running diagnostics would clear the fault. The SAR110 diagnostics always dropped and restarted the PPP session.
With newer Billion routers the status screen shows the PPP status as checking username and password, and it will freeze here indefinitely until either the router is reset or the connection is disabled and re-enabled.
I'm guessing this happens on maybe 5% of connection attempts. As the Billion routers often maintain a PPP session through a resync it's rare that the problem shows.
My problem is I'm now using a VPN bridge and I'm faced with the problem that if the router gets stuck when I'm not there I'll probably have to phone someone to reset it.
I don't think you're the only one with this problem - I think BT still have problems with "stale sessions" whereby when your modem/router/whatever drops out, it doesn't close the connection gracefully so you can't log back on for a while. Depending on what Billion you have, can you post the configuration file (minus usernames/passwords) - might just need some settings tweaking.