For those wondering: The new november update (SD1A.210817.037) does not fix this issue, unfortunately.

I might be wrong here, but I think I came close to finding the root cause.

So far we have seen reports of this issue occuring after the phone is drained or overheating. No charge = not enough for SoC to run = SoC turns off. And overheat = SoC needs to cool down = SoC turns off.

The Tensor SoC contains a security core in addition to Titan M2. The security core is responsible, among other things, for interfacing with Titan M2 whenever the phone requests verification of credentials.

Maybe a loss of power is causing some malfunction in the security core leading to it not being able to communicate with Titan properly? Because if there is no communication between the SoC and Titan there will be no fingerprints and no way to save fingerprint data (at least I'm assuming so), which is exactly what this issue is.

Or, Titan M2 might be corrupting itself, since a factory reset is the only known fix and that wipes Titan M2. Though it might still be an issue with the security core.

Of course all of this is just speculation. I don't work at Google or know how these chips communicate.