Over night battery drain, 2003 Duramax
 

I haven't had a complaint about this truck since I bought it new late in 2003. Two weeks ago I started it and drove about 30 miles and shut it down, then about a week later I attempted to start it and it was dead. My first thought was, it's winter and these are the original batteries and they are probably due to be changed out.
I changed them both out and still have the same problem.
I charge them up fully for 24 hours and it sets two days and the batteries are almost completely discharged, only enough power to light up the panel, but won't turn the engine over.
With the batteries fully charged the engine cranks and starts just fine. The amp guage shows that the system is charging and continues to show charging while I am driving. But shut it down and in two days it won't start.
Any suggestions?