Ocean 17, I had the same problem. Erase, re-fingerprint, get success, then - nothing. Following the suggestions of others that posted to this thread, I took my IPhone back to AT&T and explained the problem. They had never seen, or heard of the problem, but replaced my phone with a new one. I told them they needed to get on this site and follow IPhone threads. The new one works better, but my fingers must be dry and clean in order for touch ID to work. My thumbs seem to be the biggest challenge, but the first finger on both hands seems to work fine.
Also, there is a short period of time that AT&T will do any warranty work (maybe a couple of weeks) after the initial purchase. After that, you take yours to the Apple store and they will replace it.
Hope this helps. I agree that Apple has not got this dialed in, but biometrics are the way to go. They better get this fixed, because it is a deal breaker for anyone considering IPhone because of their touted biometric technology.
Cheers