Nope, but then we have a Honda Odyssey on a dolly.
The only time I had battery trouble with it was towing it four down and had to leave the key on in the "accessory" position.
I can't think of any reason for the battery to discharge that soon if the vehicle is turned off.
2009 45' Magna 630 w/Cummins ISX 650 HP/1950 Lbs Ft
Charter Good Sam Lifetime Member, FMCA, SKP
RV'ing since 1957, NRA Benefactor Life, towing '05 Odyssey