Clearsky,
The wire from the truck 12v circuit is tied to the output of the converter/charger which has capacitors on the output. They act as power filters, smoothing out the DC voltage to a consistant value. They charge when power is applied and if your 12V circuit has a high resistance to ground, will slowly discharge.
I would think that it would discharge fairly quickly, back through the rectifier circuit in the charger.
Does everything work with it plugged into 120v AC power? It sounds like the charger has an open rectifier.