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After sitting for a week will not start

I have had my truck, 2006 Ford F-250 power stroke diesel, since new 2006. Every winter (Alaska) my truck will not start after sitting for approx a week (give or take a couple of days). I do plug it in for about 24 hours prior to start which should be plenty. It is now doing it to me in the summer after sitting for only about 2 weeks. I am able to jump start it everytime and after that it will run/start great until it sits again. I have taken it to the dealer twice under warranty. First time they charged the batteries and called it good. Second time after being out of state for about a month or so I had to have it towed to the dealer ship. They replaced both batteries on that occasion. Next winter same issue however my warranty was now up due to time, I only have 23000 miles on it. My friends and I checked battery voltage to see if there is a draw off of the batteries both batteries checked over 12V. The only thing that I can come up with is a draw off the battery due to the fact that a jump start will get me going and if I drove it every day it would start with no problems. But it should last longer than a week or even two without the batteries dyeing. Any Ideas?