Have you checked continuity from battery positive to access2 battery positive terminal? Sometimes if there is high continuity in that cable it can throw the code. It sounds like a cable issue if the battery is testing good and the fuses are also good. With the truck operating for a short amount of time before it codes it means you can rule out the access 2 moduele being bad as it does operate. My guess with the battery loosing charge so fast, it might be shorting out to something.