The only time the battery on our toad (2010 Ford Edge) dies is when we tow it too long without starting it. If we must drive longer than 5 hours or so when we stop, we'll go run the Ford for a bit. I must say, though, that we towed a 2007 CRV for way too long (a few times over 10 hours a trip), never started it up, and never lost charge on the battery!
John & Cathy Lamb
45' Marathon XLII