Great discussion now! Cleaning th Touch ID sesor immediately restored both my and my wife's Touch ID button.
After reading some of the posts, there probably are a number of causes and so a number of different solutions. So not a one-size-fits-all solutionl. A lot of emphasis seems to be on re-scanning. I don't see much said in these posts that the Apple recommendation for proper ID sensor cleanliness is understood or is being followed. Remember Apple says to keep the sensor clean so why not? This is neither a secret nor to be unexpected.
Here are quotes from the Apple Knowledge base article http://support.apple.com/kb/HT5883:
"Cleaning the Touch ID sensor
A clean Touch ID sensor can read your fingerprint more easily. As needed, use a clean, lint-free cloth to wipe off any dirt or debris from the Home button."
Troubleshooting Touch ID
Ensure that your fingers and the Home button are clean and dry.*
* Moisture, lotions, sweat, oils, cuts, or dry skin may affect fingerprint recognition. Certain activities can also temporarily affect fingerprint recognition, including exercising, showering, swimming, cooking, or other conditions or changes that affect your fingerprint."
Here's my hypothrsis that might explain how a dirty sensor could affect reliability. Joe_Fo in the above post wrote that he re-scanned without cleaning and it only worked for a while before going back to unreliable operation. If you look at his great picture of the greasy mess, you see what the sensor is dealing with. The ID sensor is touch capacitive and is measuring extremely small differences in conductivity as it measures the small varitions in the fingerprint grooves. So it is able to create the proper scan with that greasy mess pattern. Now over time you gradually change the greasy pattern with a resulting change in conductivity. So if you rescan you get different conductivity and theregore the scan once again works for a while.
So with great technolgy comes great resposibility. This means clean the sensor, wash your hands and dry them before scanning your print. And clean the sensor periodically. And consider all the caviots that Apple has said will affect Touch ID. If all this has been been followed and you still have problems, then look for other causes.