What year Cobalt? Are you still under warranty? So if the car sits, you loose charge on the battery? Regardless of what they say, I would NOT rule out a battery or charging system issue. If it's not that, I would pull one fuse at a time while the car sits overnight to see which fuse being removed prevents the draw on the battery (eliminate one circuit at a time). I'd also remove/unplug any aftermarket accessories you have to rule them out as well.
Joel