Starting in iOS 9, a few more settings share the same configuration file that the store apps use, making the solution a little more involved.
In iOS 8, the solution to this was pretty easy: You could sign out of your account in 'App and iTunes Stores', reboot, and sign back in no problem. Is the App Store or iTunes Store app on your iPhone repeatedly prompting your for your Apple ID and password? I mean repeatedly as in, you enter it, the iPhone thinks a moment, and then asks you again, never satisfied.
