So for starters and to be clear, I have the new M2 Mac mini Pro running Ventura 13.3.1 and the Magic Keyboard with Touch ID that I bought separately to use. I went through the initial pairing steps and the keyboard itself works fine at all times but the Touch ID worked only at first and then each time after turning it off and on but would stop responding within 10-20 minutes.
Here are the steps I went through with the support rep, Steve, using the feedback from the Engineers. I also want to give a shout-out to Steve. Since it takes about 10-20 minutes to know if the Touch ID stops responding, he called back numerous times to follow-up after we went through each step.
1) Started up in Safe Mode - Problem was still there
2) He said that the Engineers noted from the logs that I had a VPN installed and, even though it was not being used, they wanted me to uninstall it completely since that can sometimes interfere. I use IP Vanish so I first trashed the file com.ipvanish.IPVanish.plist from the preferences folder in the Library directory and then also uninstalled the IPVanish App using Clean My Mac X. After a reboot, problem seemed to still be there.
3) I added a new user ("Test User") along with a Touch ID. I then logged in as that user - Problem was still there.
At this point, Steve said the next step was to check, and maybe replace the keyboard, at the local Genius Bar and proceeded to update my Case file with the latest outcomes and set up the appointment. While he was doing that, I logged out and then back in as myself and also deleted "Test User". I should note that we did not test the Touch ID again after this since we were essentially done for the night.
However, I noticed a few hours later that the Touch ID was still working and it continued to work when I woke the computer on Friday morning. After a while, I decided to see what would happen if I restarted the computer and sure enough, after doing that, the Touch ID problem was back. After turning the keyboard off and then back on, it worked and I plugged it in via USB to see what would happen. Later on Friday, it still worked while plugged in (I think that previously the issue was there even when plugged in) and I then unplugged it. It continued to work and is still working through this morning.
So hard to reach a conclusion as to why it now works, whether it was uninstalling the VPN, starting up as a different user and then back again as myself or some combination. Either way, I will take the win and avoid shutting down the computer as long as I can since having the Touch ID work consistently makes life easier. For now, I have cancelled the Genius Bar appointment.
If you are able to duplicate any of this and find it makes a difference, please post the results since it might help know which was the step that addressed the issue.