I had the exact same problem. There's no need to restore or whatever, that does nothing (and has always done nothing). Genius bar is similarly pointless.
I'm still fighting the sensor, but I basically had to keep deleting my finger profiles and retraining it until it started working 100%.
It seems to have a problem when you add more than 1 finger to the profiles, so that's why none of the reviews and what not have picked up on it.
What you need to do:
1. Delete all finger profiles.
2. Add one finger.
3. Keep locking and unlocking the phone with that finger, so it trains the sensor to accept all the variations in angle/ridges/etc of your finger.
4. Once that works 95% of the time, add another finger.
5. Go to step 3.
That's worked for me, and now my scan failure rate is like 1 in 10 (and I usually just move my finger a little bit, and it unlocks). It does work, just takes more training.
I think it has something to do with how your fingerprint looks to the scanner... my skin is pretty coarse, so it seems to take more time. My DW's unlocks every single time with zero training, and we have identical phones (same factory, same production week, etc).