One of two things may be the issue here.
# You have a shot/dead/defective battery that needs replaced.
# The iPad power management system is failing. If this is the case you will need to replace the logic board or do some intense soldering to fix the issue.
'''''If I was doing the diagnostics myself, I would replace the battery first.''''' Then test again to see if the issue was solved.
If you are still under Apple warranty I would recommend having them take care of this issue for you. Battery replacement on an iPad is a real pain. I do it, but I don't recommend it.