A few users in Apple’s Support Communities comment that Touch ID is unresponsive and buggy with iOS 9.1. Users state that Touch ID works more slowly – and frequently not at all – when updating from a previous iOS version to iOS 9.1.
Although many users on Apple’s Support Communities and a few on Reddit are reporting similar problems, it does not appear to be widespread.
Some users began noticing Touch ID performance problems after installing iOS 9.1. When they used iOS 9, Touch ID unlocked the phone immediately. With iOS 9.1, Touch ID responded much less often with manual passcode inputs frequently required. Attempts to solve the Touch ID problem with the iOS 9.2 Public Beta didn’t yield any positive results.
Some users report that Touch ID is more problematic with certain apps as well as the App and iTunes stores. Some users have problems across the board, including Apple Wallet.
Unfortunately for those experiencing these problems, there does not currently appear to be an available solution as this is more than likely a software issue.