I did not know about the 'bug' problem on touch ID.
I have heard it is happening as a problem (losing fingerprint memory) on the 6 and 6+ as well as the 5s.
It has happened to me as well and the 'fix' from Apple Care is to download the iOS again and do a reinstall .. which I have to agree with as a 'restore' will fix it .. and also the clean install of the iOS is not really a fix for me as the problem comes back again.
The times it has happened to me (once lost both fingerprints for access in one go, no idea how that happened though I was plugged into the USB chain).
Then on another occasion I lost the thumb print when I was plugged into the USB and using the iTunes over the internet to update an app.
I turned off the iTunes fingerprint authorization thinking that had something to do with it .. but as it turned out ... apparently not.
So I put in the third finger into the memory.
About 10 days later I lost the index finger print in the memory ... phone was used all day and got it home for a plug into the USB for charging.
No iTunes activity and .. bamm .. it is gone; no clue as to what is going on other then on every occasion I make discovery when the iPhone is plugged into the USB chain (as I push the home button to check Battery Doctor for charge status or answer the phone etc).
I have an appointment for the Genius to look at the hardware ... see if there is anything with that for my 5s/32... but I doubt it.
The 5s/32 works ... do a clean install of the iOS .. and it works for everything, fingerprints go in, they unlock the iPhone.
Then later ... for reasons I can not understand yet .. it just stops working as the fingerprint memory is ... not being of any use.
I am sure it is in there, just not being accessed for use.
My fix for right now .. is to enter in newer fingerprints ... delete the older one that is not being recognized and then re-enter another scan of the fingerprint image I deleted back into the system.
It deletes and re-enters so far .. and I do not have to clean reinstall the iOS as a fix.
I know this little diversion about the same issue is not a direct address to the OP ... and for that ... recommend the Apple Care fix they gave me .. reinstall the iOS and take it back to factory settings.
That do not fix it .. take it into the Apple store for the Genius if you are still on apple care as a hardware malfunction becomes more of a possibility; especially if the iOS is reinstalled at the Apple store for a return to factory settings ... to see if the fingerprint issue is still present.
If the Apple Store fixes it in that instance with their store iMac ... you have to look at your iMac set up at home for the problem.