Well shoot, my apologies if I brought the bad luck. I was on a high from fixing the night vision issue followed by the low of having the battery and power supply fail.
I wanted to share a similar experience in case it helps anyone. Like EMC, I also noticed about a week ago that my AD410 would start disconnecting at the same time every afternoon--which just so happened to be the exact time that the afternoon/evening sun set low enough on my westward facing covered porch and shine directly on the
doorbell. I noticed the same thing EMC did, a large gap on the bottom of the doorbell housing between the front and rear cover. For a few days, the doorbell would come back online after a few hours, but it eventually just stopped working one day, and I could no longer power it up with 16VAC using the terminals. However, it would still turn on via USB power.
I did my own autopsy and found the same culprit, a hilariously swelled up battery that pushed the plastic apart. I believe this battery is used to briefly power the doorbell for a few seconds when you press the doorbell button with a chime connected. Since I do not use my chime and just rely on the button presses for automations via API, I decided to just remove the battery completely by unplugging it. Also, like EMC, several plastic pieces fell out when i opened up the doorbell, which are apparently small washers for the screws that secure the two panels. I was unable to fully join the two panels with the existing screws because there was no plastic left for the screws to bite onto. Luckily, I had a couple of 1/16" wood screws that were a near perfect length, so I decided to use them to secure the panels. Luckily, it worked, and I no longer have any gap in the camera.
After reassembly, I connected it back to my 16VAC bellwire and it powered back on--no battery necessary. Here is what I think happened: The internal battery swelled up so much that it pushed the two panels apart to the point where the internal screw terminals no longer physically touched the contacts on the inside of the doorbell. I suspect that the contact had been minimal for some time, and the afternoon sun shining directly on the case created the right conditions to expand the case to the point where there was no contact at all with the inside terminals. Luckily, everythhing else on the PCB looked fine upon visual inspection, although I admittedly didn't test with a multimeter.
Note again that I would only advise discarding the battery without replacement if you do not have a chime connected, If you do use a chime, the battery must be replaced or your doorbell will cut power every time you press the button.