At this point, there is one thing that I am certain of.....every day my OBI resets itself. When it resets itself, both lines ring a single ring.
The time it resets itself is the time that it was last rebooted. Unless I make a change that requires rebooting, it never is rebooted. And I have it, and my router, cable modem, and other network equipment connected to a UPS so it is not effected by power outages.
I have the OBI connected to another router. The DHCP lease time in the router is indeed set for 24 hours. So, to test infin8loop's theory, I have this morning set up the OBI to use a static IP address, at right at 10 AM.
I will see if the thing rings tomorrow at 10 AM and post the result in this thread.