Similar to my problem with the 3210 - except that mine always stopped on the wire. Kyodo saw that the motherboard was incorrectly reading the voltage on the battery - and so it would shut off thinking it was out of battery - even though the battery was at 2700. They replaced the motherboard.
The behavior of not being able to power on again is consistent - once the voltage is below the threshold, no button will get it to come on again until you put it back in the charger.
Something must be draining the battery before it can return home. I have noticed on occasion that if the robot gets stuck on my hilly lawn, spinning the tires for a long while, then it could run out of battery before it gets home - but usually i just find it stuck and displaying "blocked".