I got the same problem yesterday , and try to fix it, and contact apple support. There is no right solution from apple support till now.
I try to use DFU (Default Firmware Update), and select "update & backup?" . The meaning is something will be lost from the current ipad.
After done, my iPad is updated to ver: 9.3, and all data lost.
Then go backup with the latest backup data .
After backup finish, there are some apps need to update the latest one from App store notice.
There is Apple ID request popup, and ignore it, and then activate request popup, iPad is locked again around 20~30 mins.
Do the above process as DFU again, and iPad is locked again around 30 mins.
I try to remove some old APP (around 70 apps) from PC.
Do the above process as DFU again, now my iPad is alive without activate request popup. Alive 9 hours.
It seems Apple server verify app with auth failure issue.