Not sure about the 2005 but my 2013 F350 diesel has a battery disconnect built in. There is a parasitic drain on the truck battery from things like clocks and other electronics but that shouldn't be an issue in 3 months time. I assume you have two batteries since it is a diesel. I keep my truck on a battery tender because it is often months between trips. Disconnect the battery terminal and measure the current draw with a meter. That will give you some idea of how large a drain there is. That is where I would start my trouble shooting. If there any significant drain something is amiss somewhere.