This could be caused by several different things. Please let us know more about the history of the device.
My initial suspicion would be the battery. The device is now 4 years old and the battery could be at the end of it's life. To be certain, use a battery utility, such as coconutBattery (for Mac) or 3uTools (for Windows). It will tell you what the health of the battery is. Anything less than 70% of design capacity will require replacement.
If the battery is fine, then it would really depend on what the iPad has gone through in the past. Was it dropped or damaged (dented corners), came into contact with water or previously repaired. These can cause logic board issues.
The other thing that I would try is a full DFU Restore. This will completely over-write iOS and all data. It will be factory fresh, so to speak. That would eliminate any potential software/data corruption issues.