Okay, here's a bit of data for you:
Battery: Single 12V Group 24DC
Solar: UPDATE: I have been victim of false advertising by Coleman/SunForce. The kit I bought clearly advertised an 85w panel, but I have since looked for the same kit and it says 15 watt. Reviews on Amazon confirm same. Spent $120 on that kit and for that price I almost could have had the Renogy 100w kit. Sigh.
Inverter: Xantrex X1000
Refrigerator: Kenmore 4.4 cu ft mini fridge
Started the fridge halfway cooled (it was cold and sat without power for 1 hour) at about 11 am. It was a warm sunny day, about 80 degrees. Battery read 12.73V. According to the chart here, that is 100%
http://www.solar-electric.com/deep-cycle-battery-faq.html#Battery%20Voltages (voltage readings are a little skewed due to solar input).
At 11 am the next day, the battery was down to 12.06V, which is 50%.
So, 24 hours ain't bad. If I could get 2 days, that would be fine, as we rarely stay in one spot for more than a weekend, and the TV can charge the battery after that.
Granted, this is with no load from other appliances, such as lights or water pump. My conclusion is that the battery capacity is sufficient. With more solar capacity, I think we could gain a couple of days before the battery needs a charge from the TV. What do you think, would another 100w panel do it?