Well, I've read through this entire thread in search of an answer for my own touch ID problems. I'd like to share my findings in a way that doesn't prompt Apple to delete my post -- when I recently tried starting a new thread with my problems, they imediately deleted my post, claiming that I was starting a poll (not true, of course). I'm just hoping against hope that somebody, somewhere, has an answer for me.
THE PROBLEM: It's exactly the same as described elsewhere. No matter how carefully I register my fingerprints, my phone forgets my prints within a few hours.
SOLUTIONS I'VE TRIED INCLUDE:
1. I've tried erasing the phone and setting it up as a new one. I have done this several times, which is quite a tedious task considering that I have over 200 apps, organized into folders. NO JOY.
2. I've tried registering my prints differently. I have tried several different techniques, including the one detailed so excellently by Joe_Fo. I have also tried registering just one print five different ways, registering five different fingers to see if one will actually work, etc. NO JOY.
3. I've tried swapping out my phone for a new one. The wonderful folks at my local Apple store have actually done this for me twice. Each time, I set up the new phone as, well, a new phone, rather than restoring from backup.So I have now had the depressing experience of watching my touch ID fail on three different phones. NO JOY.
4. I've tried scrubbing my hands squeaky clean. I have then tried and registering when my fingers are slightly moist or completely dry. NO JOY.
So I think that takes care of every "cure" described here or elsewhere. None of them work for me. But I HAVE noticed some clues that may lead to a real cure.
CLUES:
1. I can make my phone forget my finger prints INSTANTLY, and fairly reliably, by playing a video while uusing a navigation app -- in other words, making the processor and memory work hard.
2. I can make my phone "remember" my fingerprints a bit better -- not forever, but a bit longer -- by using an app called SYS-ACTIVITY or SYS-LITE. It's a terrific utility which, among other things, can create about half a GB of free memory. I thought at first that this app, used several times a day, might be my cure. Alas, no. But it does help a bit.
SO WHAT IS THE CURE?
To go any further, I would need to be a software engineer, and alas I am not. But it does seem to my unschooled brain that the failures are probably not hardware-releated -- at least, not for me. I must believe that the act of fingerprint-recognition is fairly processor-intensive and demanding of memory. And I have read that the print-data is cached in the processor. So there MUST be a bug that can be triggered by using demanding apps together -- ESPECIALLY apps, like video podcast catchers and maps, that are allowed to multi-task in real time.
I don't believe this problem is confined to just a few of us. I've heard from too many others with similar problems to believe this.
This gives me hope that someday my problem might be fixed. Meantime I'm miserable. The only reason I sold my iPhone 5 and bought the 5s was for the touch ID, and now it doesn't work. If anybody has a fix that I haven'y already tried, I'm dying to hear it.