Broompilot's story reminded me of a feature we have on our setup that all trucks should have, I belive. If you are spec'ing a new truck or generator, ask about it.
If the generator does not auto start for some reason, the sleeper will continue to draw power from the truck batteries via the inverter. If the inverter detects that battery voltage is below an established level, the inverter will shut down all power to the sleeper, leaving the truck batteries healthy enough to start the truck. The milk in your refridgerator might get warm on you, but you won't have to find a buddy to give you a jump or pay for a service call.
By the way, one of the things I like about having a reefer is the ability to jump the truck off the reefer battery if need be. The truck may be dead, but if the reefer and truck electrical systems are kept totally independent, one bad system will not drain both down. You can jump one off the other.