This has happened to me today as well, i got the phone friday morning and its worked fine all weekend but today it stopped recognising any of my recorded prints
I cleared the prints and tried to record new ones and it took multiple attempts to get a successful print recorded (in the shop it took like 5 taps to get the whole print then moved onto edging) but now it more often than not fails to record a whole print and i have to start again.
As of now i have no prints recorded and cant successfully record new ones (it gets the whole print other than one of the three central lines of the fingerprint and then refuses to store them right up until it fails)
During the process of troubleshooting this today the few times it has allowed me to record a print and enter the phone via touchid it has taken much longer to do so than it had been when it was working properly (4-5 seconds to successfully read the print)
I have the white one and it's presenting the exact same problem as some of you are experiencing with the black
I've found that if you are a little sweaty or handle something plastic (Xbox controller, garbage bag ect) then it stops working, I've also found that if it doesn't work with dry hands clean off the sensor with a glasses cloth or something and it works first time
Apple tech support did tell me there was a software issue making this happen but I'm not sure about that it's possible though because it worked perfectly for 3 days and I have to assume I had sweaty hands at least once in 3 days - it got unreliable after 7.0.1