Arduino shuts off and doesn't turn on after couple hours
I assume your charger is connecting to the USB port of the Mega2560. 

That USB port has a polyfuse (actually a special type of positive-coefficient thermistor) which is normally rated at around 500mA (polyfuses are a bit woolly with their ratings since they are heat based).

If you are drawing near that limit of current the fuse will be gradually heating up. I would think that after 10 hours it may have reached its threshold temperature and thus switches the power off.

Disconnecting the power and allowing it to cool down would then make the board work again.

How can you test it?  Well, next time it switches itself off try bypassing the polyfuse (tweezers would be good to do that with) to see if the power LED turns on again.