iPad Mini 2: iOS 9.1 iMessage doesn't work after restart.
It sounds like this is a bug. You should probably report this to Apple Support.

Try to sign out of you Apple ID, then force restart by holding down the Sleep and Home buttons until the screen goes dark, and release. Afterwards sign back in to your Apple ID.

If this fails, try making a backup in iTunes (download) then restore to the latest firmware. This does two things:


It "reuploads" all the settings on the iPad Mini 2 such that any weird setting bugs should be fixed.
It updates the iPad Mini 2 to the latest iOS firmware possible. Take note that usually there are multiple bug fixes in every new itieration of iOS firmware released.


I do not guarantee this bug will go away, but you should give this a shot.