If everyone keeps posting the same thing then this is going to go nowhere.
At the moment there are 2 problems...
1.Your finger print stops working or it takes a lot of attempts. You get asked to "try again" a lot.
2. Sometimes, randomly, the phone doesnt respond. It seems like the scan worked, you do not get asked to "try again" and it wont unlock until you enter passcode / or it has unlocked and swiping takes you to home.
Both of these can easily be software based. Swapping hardware numerous times will not help you and it would be best to wait for the next software fix.
This is new technology and its the first time its been in the wild like this. I do not think a similar tech / finger print scanner was pushed to such a wide user base in such a small time, and after some very secret and small scale testing.
Possible identification of the 2 points above
1. The software is messing up over time. As a programmer its quite easy to have code that looks like it works, but when the sample data is replaced with real world data, other bugs show up. As the phone tries to learn more about your finger it could be corrupting the stored data and as such, eventually it's record of the finger print doesnt match the actual finger print.
2. As this only happens very randomly and doesnt not correspond with the loss / corruption of stored finger print info this must be a software bug. Apple has had so many problems with the unlock screen over the years, multiple bugs, that is not a leap to consider this another one. This will helpfully be addressed as well as TouchID is improved.
You have a 1 year warrenty and so it might be best to wait a bit. The first batches of any hardward product usually have both hardware and software issues which are fixed in further revisions, not like iPhone 5 > 5S, just small revisions in hardware design or the software controlling it.
People must also consider that this came with iOS7 which has lots of bugs as well. Older apps are causing crashes, memory leaks and other problems. The OS seems unpolished in places.