i have the same problem, been restore the phone to 7.1 for the second time, choose start as new, able to add fingerprint, then testing the touch id to unlock the phone= success, later on after install some apps, music, video and photo, touch id not working at all (cannot unlock the phone -- phone unlock on setting is on, cannot add fingerprint cause the touch not responding at all)
is not like after updating to 7.1 the touch id not working at all, but after installing some apps, it didnt work at all
sorry for my english
update: connect the iphone to computer, voila touch id work again, able to add fingerprint, unlock the phone work again, disconnect the phone from computer, touch id not working at all