Another one for the files:

My 2820 lost line sync and then went into 30-45 second cycles of resyncing, starting PPTP, waiting for 10-15 seconds and rebooting.

Turned out to be Coms plc (UK), who had turned on their 'walled garden' feature to block further internet access for bill non-payers..For some unknown reason their system had flagged a one month bill non-payment for September 2013 and this is what started the fun and games.

I only found out the cause of the problems when, after some initial kit checking, and a phone call to Coms, I replaced the 2820 with a 2930 + Vigor 120 that I happened to have on hand (as you do!) and this got me online and to the 'Walled garden' page.

My suspicion is that the 2820 does some kind of online check during the PPTP negotiation phase and this was failing, causing the time out and reboot. The check mechanism on the 2930 must be different.

TL;DR: If you get wall gardened of somehow blocked from full internet access, your 2820 might go into a reboot loop.