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just had my 6 replaced because Touch ID was doing exactly what OP described, every time, not matter what I did. testing the new one now.
 
I had an iPhone 5s. The Touch ID worked okay and when Apple did a software update to iOS 7, it worked better.

With iPhone 6, Touch ID is amazing & fast. I literally only remember having two times it's given me an error.

I am definitely not an Apple fanboy (I hate the iPhone 6 design - I think it's the worst iPhone released), but Touch ID works amazing (and Apple Pay is fantastic while I'm on the subject).
 
Touch ID has worked flawlessly for me so far on my 6 plus. I can't remember it ever failing. On the 5S I'd say it worked about 90-95% of the time.
 
I find the biggest problem being MY change in fingerprints. The cold weather in the northeast has killed my hands and really chapped my fingers. So that will definitely lead to a change in fingerprints, and that DEFINITELY affects Touch ID accuracy. I find I really need to recode my fingerprints every few weeks in the winter, but in the spring-fall, it was fine for many months without issue. Seems to be better on my personal 6 than my work 5S, but I do have the issue with both.
 
I have 4 different fingers mapped in my TouchID and they all work equally well. I really haven't had any issues with it, even back on iOS 7.0 on my 5s.
 
I find the biggest problem being MY change in fingerprints. The cold weather in the northeast has killed my hands and really chapped my fingers. So that will definitely lead to a change in fingerprints, and that DEFINITELY affects Touch ID accuracy. I find I really need to recode my fingerprints every few weeks in the winter, but in the spring-fall, it was fine for many months without issue. Seems to be better on my personal 6 than my work 5S, but I do have the issue with both.

Have two prints of the same finger stored, once in the winter and once in the summer. Do not delete the other print.

Another poster indicated that it can re-learn your print in settings > TouchID. Rather than re-enter your Winter print from scratch every few weeks, tap the home button while in this setting and the entered print (Finger 1, etc.) will flash. Keep taping until it flashes more often, indicating that it's re-learning your drier print.
 
My phone was built in week 39, which is October, and I purchased it this month.

There are people who feel that it make a big difference in what week your phone was manufactored

Thanks! I was confused & thought he had 2 6+, one bought in the 39th Week and the other on the 4th of this month. My bad :)

As for the difference in the iPhones, if any, depending on what week the phone is manufactured - I do believe that there would rather be a descending trend in the number of issues in the newer devices and not the other way around (but of course Apple cannot address such issues without notifying the public for that would go against FCC guidelines)
 
My iPhone 6 works perfect for me

This online research what did you find out?
A few random posts on the apple forums

Seems it's working as it should for millions
 
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