Final answer to this mystery:

Known bug in the Arris firmware. The issue is that there's something wrong with the DHCP negotiation in the final stage of registration. The problem is permanent, and can't be fixed without just replacing the modem.

By "known bug", I mean, it was a bug that's been occurring for years now and only recently (last 6 months) did the comcast techs finally understand it to be an actual bug that made them keep having to replace Arris modems. Supposedly, according to my tech, Arris has acknowledged this bug. Now, since Comcast supplies the firmware, I don't see why they can't fix the bug and push out a new firmware rev, but I don't understand how this stuff works on the back end.

Turns out it's the same bug on TM822G and TG862G models. My problem is that my selection of available models is very narrow due to my VOIP land line requirement, so I don't have a lot of choice in this area. On amazon, there are very few VOIP capable cable modems that I can get which are fulfilled by Amazon (I've had trouble with buying items from "amazon sellers" for orders which aren't "fulfilled by amazon", so I try to avoid those). So when I had decided that I wanted to order from amazon and get the modem overnighted, I was left with, like, two models that were on the comcast approved list. So if the bug was in a narrow range of models, and I was stuck buying models in that range, it's no wonder that it looked like an unusual coincidence that the made it look more like malice than bug.

I've ordered, from a less-reputable seller, a different VOIP model from SMC in hopes that it won't have the same bug. Only other kind I could locate.