Well, my turn...
I've been watching this discussion since the beginning and appreciate all the ideas everyone has, as crazy as they might be, you never know when you'll stumble upon something that you've never tried. 😉
I got my 32 Gig iPhone 5s (unlocked) in early November, so I dropped a lot of money on this thing. I always purchase factory unlocked iPhones. I didn't get it specifically for TID, but I did want to use it and have it work. There are some locations that I travel to, where I use a complex passcode only.
Initially, my prints lasted about a week and then degraded rapidly. I came here to the discussion groups and saw others with the same issues. I methodically tried almost every solution that all of suggested, using a text file to record and document each method. I scanned and rescanned using Joe_Fo's advice (which I think is probably the best way to do a scan) and Griswaldo's anti-static theory, and many of the other's advice, too numerous to name. I tried the install as New phone, completely wiping it out and leaving it factory fresh for about a week, with no other apps present... same thing. I do suffer from dry skin, not excessive, but maybe drier than normal. But, I tried cleaning the sensor each time, cleaning my hands, skin lotion, no skin lotion... all with no luck. And, I tried mulitple scans of each finger, different fingers, all that stuff.
Finally, in late December, I asked my local Apple store, where I purchased it, for a replacement, which they did with no problem. Took it home, started the whole procedure over, and this time... wait for it... my scans deteriorated within 24 hours, even worse than my original phone. Again, I went thorough all those ideas that I had tried before with no luck.
Seeing that many of you have had several replacements, and still having the same issue, I'm more inclined to think it's a software issue and hopefully it will be addressed. But, I understand how frustrating it is, and as Doggyluver said (I'm a doggie lover also, have three!), it's just easier to use my passcode all the time, and I've been doing that since my 1st gen iPhone, so it's no big deal.
I've never had anything to add to the discussion, I think everyone has beat this horse to death. But yesterday, while waiting for a client, I was bored and decided to try it again. So, I closed all apps and restarted (I usually do it like this, but have also not done it like this), and using JoeFo's method, rescanned my thumb print. And yes, after a few hours, it quit. But, in desparation, I moved my thumb way up on the sensor and it worked. And today, it worked again. I honestly don't think I scanned my thumb this far down, almost to the first joint, but this has lasted longer than previous attempts. When I go to TID in Settings, it will not light up with the areas I scanned, but if I go further down, almost to that first joint, it will light up, and it will unlock the phone. It's kind of the widest area of my thumb, just above that first joint.
Again, this just may be another abnormality that goes away tomorrow, but I'll keep training it for a few more days and if it lasts, I'll report back. I've also given Apple feedback on this, so hopefully, whatever issue is going on, will eventually be addressed. For the record, I use a Magpul slip-on case, with a cheap screen protector (although I've tried it "naked" also).
Thanks to all for your ideas and perseverance, hopefully it will pay off.