I've seen that with iPhones as well. When the battery goes bad or is faulty it jumps around in %'s and then can die randomly. Not sure about the logic board, but I can't imagine that's not bad."
"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."
I found what causes the problem you are describing. Next to the battery connection on the motherboard. There are 6 resistors. When disconnecting the battery it is easy to displace one.(as I did) as soon as you power on and run for awhile the OS checks the battery level the pad reboots and then the percentage of battery life changes.