That isn't true... the car is "supposed" to turn off after a while (as in 30+ minutes) if the car is left in Acc. or something like that. Supposed to save battery. I know, I've left the dome lights on by accident and the car turned everything off eventually...so the next morning I was able to start the car with no problems.... and then turned off the dome lights.

 

The Smart Key system has a very small drain and should not have caused your problem. It sounds like you have a bad battery. It happens, as I've had it happen to me on a new vehicle. Batteries that seldom get used are well served by an intelligent charger. I always keep my motorcycle on a BatteryTender and it is always ready to go.

 

There is some truth to the battery draining faster with the fob in the car. There is a fairly elaborate power saving scheme for the smart system as long as the fob is out of range, starting at 7 days with complete shut-off of the broadcast pulse at 21 days without the fob in range. There's a whole big section on it in the factory service manual. If the fob stays in range, it will definitely use more power than if it is not.