Does it try to download/install new firmware immediately after initial setup?
I believe that it does - at least I believe that mine did. During initial setup it went through all the motions and said it was connected to my WiFi but shortly afterwards, it disconnected. I re-ran the setup and it reconnected and it's been connected for the last several weeks with no issue. I suspect the initial disconnect was because as soon as it connected to my WiFi it found a firmware update available and ran the update and I caught it doing that which is why it disconnected and put me back through the setup.
I believe the firmware updates trigger a restart of the doorbell, which causes them to temporarily disconnect from WiFi and then possibly check for any new update after reboot.
As with firmware updates for any device, an interruption during the upgrade process could brick the device.
Unlike Windows, mobiile apps, web browser, etc software updates, there is no option to delay, defer, or pause firmware updates for the Doorbell Pro by the end user.
Sounds about right to me. It's great when it works but I've been having a bad stretch and no longer recommend this device which makes me sad because it's really got a lot of good to it but it's been unreliable after the first year.