Well it is a few days in and the H25 receiver seems to be staying on so far. No idea if it is still going down in the middle of the night or not. If it is, then it is also able to recover on its own. I will eventually find out.
It did have an interruption at least once on the first night, but I didn't think to reboot the HR44 before that, considering the addition of the H25 on the same satellite dish and hence the same "network". Maybe that was a factor, maybe not.
I still am trying to learn whether or not the H25 reboots, or at least interrupts the video feed, on its own in the middle of the night to download its schedules (as I seem to remember the single tuner Tivos did years ago).
I did block all the interactive settings on the H25, so that it doesn't try to do anything with the HR44. This is under "Whole House" settings on the H25 menu.