I got the same fridge and ran it off my starting battery it worked fine until the fridge died (only lived about 3 months, they refunded me quickly though).
But when I used it I was moving quite a bit not staying in one place. I don't think I could have gone more than 24 hours without the fridge shutting off due to low voltage.
Since then, I've put in a AGM battery and 100W Renogy panel and 20amp Renogy Rover controller and I've got it so the house AGM battery charges when the starting battery is full while I'm moving. This setup has been ideal as it keeps the house battery topped off in the sun and while moving. My house battery has stayed charged.