I have the 2011 QX56 and I've seen something similar. The battery is new. If the headlights (set to auto) are on, I can't start the car. Looks like the battery is not fully charged but it's been charged overnight.I have a recurrent problem. Once a week or less frequently, I go to start the car, and the battery is dead. Battery voltage is at around 8.5 volts. Battery is new. Alternator is putting out about 15 volts. I jumper the car, it starts, and the alternator pumps out about 15vdc, the battery comes up, and I’m fine for another week or two. Anyone have a similar problem?