I recently replaced the battery of an Ipad 3 4G using a "non-apple" battery, and experienced the same problem. The Ipad did not recognise the battery level, and rebooted every 2-3 minutes. After every reboot it showed a different battery level, and on the lock screen it didn't show that it was plugged to a charger. So obviously it had to do with the battery gauge...
After making sure no damage occurred while working on the iPad, (Motherboard) I ordered an original Apple Battery and replaced the non original.
That solved the problem immediately, now it's charging without reboot and everything went back to normal.