My tablet shuts itself down at any given moment and then can not be rebooted for at least 10 mins.

Try to do a hard reset, The 10" Irulu has a reset on the right bottom edge. You'll need to stick a sharp pointy pen that fits in the in the small hole, push. Press the ON button and see if it starts. Resetting will change the time and date to the default setting of your unit.

Pull Battery ,,let sit for 10 mins ,, then install ,,reboot

the reset button is the power button on the tablet you just hold it down until the tablet shuts itself off.

samsung galaxy 10 2.1 keeps rebooting and rebooting automatically. Displays going into power saving mode and reboots. stays on for aobut 10 seconds and then shuts down. Will not take a hard reboot. Help

By holding the power button down for about 10
seconds it rebooted
baw

Turn the tablet all the way off, press and hold the VOL - and power at the same time for 8 to 9 seconds, it will show a green android guy with a system recovery menu. Use vol - to go down to Wipe Data/Factory Reset, press the power button to select it, go down to 'yes' to confirm, press the power button to select it, it will wipe the tablet, you then press the power button on 'reboot system'.

its better you should reinstall the os or repair it using recovery option

Have you tried resetting the Pandigital. There is a small hole that you can put a paper clip in and it will reset the reader. It will take a few minutes to reboot after you press the reset. You should also go to the Pandigital site and update the reader. I have attached the link to there site.
Thanks for using FixYa
http://www.pandigital.net/Downloads

By holding the power button down for about 10 seconds it rebooted

If you haven't already done so, you have to download the Pogo application from the iTunes app store. If your problem is with the app itself, the first step would be to reboot your device. To reboot the iPad, hold down the button on the top of the iPad until you get the option to shut down the device. Once shut down, press the same button to power on the iPad. Test the Pogo app to see if it works now.