Has anyone tested for parasitic draw on these problem vehicles and compared them to the manufacturers acceptable numbers? If its not a bad batch of batteries there may be a bug in one of the computers not shutting down a component in the system.
This excess gas fouling your catalytic converters. Repeated cold starts can exacerbate this during open loop cycle as the engine is dumping gobs of fuel before entering closed loop. Moreover, with only a couple hundred miles your ecu is still learning your driving habits and will lean out fuel...