Was this after the 9.2.1 update?
I did go to the Apple Store yesterday and here's there response:
The ran several tests on the phone remotely, which turned up no issues. They did note the abnormal battery drain, confirmed my settings were perfect, and had no explanation.
They then suggested it might be a firmware problem, and reset the firmware and one again restored the phone as new.
While that did not resolve the issues, they retested it and discovered a minor battery fluctuation. However, they ruled that the battery was in such good condition that they could not authorize replacing it -- despite diagnosing it as a potential cause, or contributor to the problem. Although they did note a battery drain of approximately 10% within 5 minutes of performing the restore. In addition they took the iPhone apart, determined there was no visible internal damage, and re-seated the Touch ID and battery, to no avail.
The only explanation they offered was that the 9.2.1 update uncovered a preexisting hardware defect, which they could not diagnose, which caused the Touch ID to fail, and battery life to drain rapidly.
They only offered one solution since the phone was technically out of warranty -- repair the phone for $269. Or trade in the phone as-is and receive $200 put toward in-store credit.
Now I say technically because of this: The iPhone 5S was originally purchased over 2 years ago. However, it was replaced under Apple Care warranty in November of 2014, with a brand new, manufactured-phone-for-replacement by Apple. So the current phone which exhibits the acknowledged manufacturing defect, is only 14 months old, barely two months out of the standard Apple 1-year warranty. Unfortunately the phone was no longer eligible for Apple Care because it's tied to the original purchase, not to the brand new replacement phone, and I did not originally purchase the phone, so Apple Care was no longer offered when I received it.
So after spending an hour at the Genius bar, Apple has officially told me that iOS 9.2.1 broke the phone, which they presume suffered from a physical defect, and despite only being 14 months old, for which Apple Care which could not be purchased on the replacement phone despite being brand new, they are not obligated to repair or replace anything.
So the official verdict -- iOS 9.2.1 broke my 14 month old iPhone -- specifically dramatically reducing the battery life, and permanently disabling Touch ID.
Well, here's hoping they don't know what they're talking about and iOS 9.2.2 repairs whatever 9.2.1 broke.