I have the issues while going to connect or disconnect Charger. When the battery indicator of my Nexus 10 gets red waring, I put it into sleep mode and plug in the charger. However the tablet shuts down itselt. That also happens after charged overnight. I remove the charger, it display 'empty red' status with battery life and then shut down. Doing a factory reset is not working. Try with other android phone and everything works fine.
I notice that many users reports the N10 shut down many times without any reason. It seems the original accessory doesn't fit the N10. If I switch to my Samsung Galaxy phone charger, the problem is solved. That should be a hardware issue. The best way is to call Google and get replacement.