If you had a piece of bare wire touching the car (ground) i would think that you would have a pretty major electrical problem. That would cause it to discharge pretty quickly and/or possibly ruin some of your car electronics. I might be completely wrong though. It dosnt seem like its an alternator problem, because it is discharging while the car is off (atleast thats what I got from reading your post). If it was an alternator problem, it just wouldnt charge correctly.