Well, here's what may prove to be a a very intriguing new piece to this frustrating puzzle! Very curious to hear if others can concur with what I've discovered. But first, a bit of background:
I've been following this thread since early November, and have been using the Joe Fo method of registration for my right thumb only. I still see deterioration in recognition after several days, and finally have to re-register again, but this has been far better than any other method.
Recently, I read about a method here for improving deteriorating recognition--i.e., when the recognized area of the thumb starts getting smaller--without having to delete and re-register, and it has worked really well so far. Simply go into the Touch ID settings, touch the registered finger to the sensor, and wait for "Fingerprint 1" to be briefly highlighted. I do this a few times, and it seems to restore recognition as if I had just re-registered. BUT... that's only part of the story...
Here's what else I've discovered: whenever I go into Touch ID settings and touch my registered finger to the sensor, it ALWAYS recognizes it... always, 100%, even after I've been having trouble with deteriorating recognition. You can tell it recognizes the print because "Fingerprint 1" becomes highlighted. And I have done this right after a bout of the sensor refusing to recognize my print. Even stranger, it seems very forgiving of how/where I place my thumb on the sensor. In short, THIS is how the sensor should be working in actual use, but doesn't...
So, my hypothesis: the sensor reads my print MUCH better--with no failures, in fact--when I'm in Touch ID settings than it does at other times. This would certainly bolster the argument that this a software issue. Please give this a try and post your results.