I don't know anything about the ipad's, but the sounds of it is a hardware issue. It sounds to me that the psu is messed up; the shutdown is often an issue with heat or of course no power at all. I would assume with such a small device that if heat were the issue you'd probably know based simply on the feel. Also, heat shutdowns are often progressive, so if you power it up and it shuts down in say 2 minutes, then you power up again it shutsdown in 1 minute, then 30s, etc. That doesn't sound to be the case here.
Although with something like an ipad, I suppose that since the psu is fully integrated it could have some software controls (thinking like a UPS here) that for whatever reason seem to think that the power is gone and initiating a shutdown, but ultimately to me it sounds to be a psu problem itself (UPS' I believe typically shutdown via executing shutdown commands, not just hard shutting them down which would defeat the purpose, and that doesn't sound to be the case here). If it were me the first thing I'd do is wipe it clean and start again in case it is a software issue. If it persists, I'd then contact apple support.
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