My mom is on her third 5S now. When she told me the second phone was still having trouble with TouchID, I thought maybe it was something weird with her fingers. I went with her to the Apple Store yesterday when she exchanged for the third phone. I watched her set it up, and it worked fine all day yesterday and this morning. Suddenly this afternoon it quit working again. It will not recognize her finger and keeps saying to Try Again. This was the same way it worked with the first two phones. They worked fine for a day and then quit until redoing the fingers as a new fingerprint. I had her setup TouchID again today, leaving the old finger on there. It worked great for an hour and now it won't let her in again. Entering her password doesn't fix it. Once it stops working it's done and never works again. I have no idea what the problem is. I've had my 5S for two weeks and I've never had a problem with TouchID on mine. It lets me in immediately every time.
I use Twitter and don't have a problem. My mom doesn't use Twitter and has trouble. I need to ask her what apps she's using when it quits working though, just in case there is an app causing it.