Inverter draw from battery for residential fridge

I am trying to figure out a couple things on this. We have gone to Florida and the fridge stayed on for each day of the trip there. So the truck must be recharging the battery as I drive it, but then on the way home, the battery went low (eventually bad) and the inverter shut off. I did go buy a group 27 instead of the group 24 but now I am thinking I should have gotten the 6 volts or a second 12 volt but I am not sure another 12 volt will fit in the space.