iPad stuck in a reboot loop with flat battery
Our iPad is stuck with a flat battery. When it's plugged into the wall charger, it reboots in about ten seconds, and we get a brief flash of the "slide to unlock" screen that dies so promptly that we don't even get a chance to touch the slider. After ten seconds or so, it tries again.
It gives the impression of exhausting what little battery charge it accumulates.
I've tried putting it into DFU mode with iTunes. It connected, but the battery didn't last long enough for that to help.
Is there a way to stop it from rebooting, e.g. by turning it off without it first having to start up?
Or some other way to give it enough charge so we can turn it off the usual way?
Any knowledge of how it manages to get into this state? We've never experienced this before — until yesterday, it was our one and only crash-free computer!