Maybe it's just that your battery is getting old. I think that this kind of flakiness is pretty common for an old battery.

Maybe I should try the cardboard approach. I tried putting duct tape over the bottom and it hasn't seemed to be enough to avoid glitches.

This issue has been a major irritant to me. When my N810 is on, it runs great. But if I reboot the system (e.g., b/c the desktop freezes), then it restarts for a couple seconds and then shuts off. Similarly, if I power the device down and then turn it on again it restarts for a couple seconds and then abruptly powers off. In order to boot again, I need to plug it into the power supply, take the battery out, replace it, push it into the connectors as hard as I can, and power on. Once it has successfully powered on, I can replace the battery cover panel. But if I have to start up away from my power cord... forget it. Sounds bizarre, but the behavior is very consistent. I can give a more exhaustively detailed account if that would be helpful. It's possible that there is some interaction with the boot menu as I am dual booting.