Mine is protected by an UPS which services all of the computer equipment in the area where it is located. It's probably good for an hour. After that, I'd probably have my generator online if I were there.
When I considered cutting the cord to the landline and replacing it with a VoIP solution, a protracted power outage was probably the most serious scenario: Not only would it likely be widespread, but it will kill my ISP in about an hour as well. However, in a pinch I have my cell phone as a backup.
I have a friend, BTW, who is running his OBi200 off a 12.6V trickle-charged battery. So far, it's run fine.