I live near Atlanta and I get the same issue around the same time. It's not reliably every night (thankfully, since I'm on almost every night) but it is at least once or twice a week, sometimes more, for 15-45 minutes. I can see in the modem logs where I'm losing my connection to them and the house phone also gets disconnected.

I'm in the same boat as you where making the phone call feels like a huge hassle. But it's interesting seeing a few other people with this same problem, maybe I should call them after all.