Apple ID asks for password continuously after updating

Keep closing the password message by tapping cancel.  You may have to do this at least once for every App you have downloaded under your account.  You can also try powering off your iPad fully for a few minutes and then power back on.  Once you are able follow these instructions:

1. First go to Settings -> “Touch ID & Passcode”
2. Turn OFF “iTunes and App Store” under “use Touch for”
3. Then go to Settings -> “iTunes and App Store” -> Password Settings at the top
4. Select Always Require at the top, authenticate if it asks, then select Require After 15 Minutes. And then authenticate again. Sometime two or three times.
5. You should then be able to switch Require Password OFF.
6. Wait a few minutes and switch Require Password ON.

If the constant prompting comes back leave "Require Password" OFF and see if it stays away.