First, this is Joe_Fo's technique:
Joe_Fo wrote:
Enroll a small area of a finger. Try to unlock far enough away from that area and convince yourself it is not working. Either go into the add a print screen or simply use the sleep/wake button to sleep/wake or highlight in enrollment screen, depending on which way you decide to prove it works, and:
1. Unlock with known area, then hit sleep.
2. Slightly reposition finger moving away from known area, but not so far that you move completely off of it, maybe a little less than half the home button diameter. A slow creep is what you want to do.
3. Rinse and repeat step 2, slowly moving towards area that was not recognized after the initial enrollment.
4. In the previously failed area yet? Is it now working? It should be.
There are a few other suggestions here, including reinstalling your OS, as described here by mrsnork:
For those still having problems, I can almost guarantee you that a restore from DFU mode will fix it. Transfer all purchases from the phone to iTunes and back up to iTunes first. Here's how to put the phone in DFU mode when connected to your computer via iTunes: https://discussions.apple.com/thread/5409794
Restore the phone and set up "as new." Go through the steps to set up the phone, including enrolling you finger print. Once the phone is set up, go back to iTunes and restore again, but this time use your backup. This will put the phone back the way you had it, and you will not have to enroll the print again. Now TID should work flawlessly. I can't vouch for multiple print enrollments, but for just one finger this works for me 100% after the 7.1 update.
Otherwise, if you haven't done so already, read through this thread starting about page 68 where IOS 7.1 update is discussed. There may be more ideas for you. The last thing is an appointment at the Genius Bar.
Good luck.