Kevin,
There are a lot of variables when it comes to the amount of amp/hr used by your batteries in a day.
Just the fridge by itself will use somewhere between 25- 60 amp/hr per day depending on ambient temps, door openings, inside temp settings, replacing cold food with warm etc.
What are your other non - fridge draws? These all have an impact how often if any you will need to use other power sources other than solar to replenish your batteries( genny, shore,alternator).
We have 4 years experience with the 7.5 cuft NovaKool 12/120V fridge/ freezer.
Started out with 4 6V AGM with 190W solar. Our camping style is 98% dry or Boondocking. Ran our genny only a few times in those 4 years. We found that with 190W solar, if the desert temps got over 90F in the day, it was touch and go so we added another 140W and never have a problem with batteries being run down.
To answer your original question, between 2 and 5 days depending on conditions.
I would recommend that you install a minimum of 190W of solar. If you have more room or even if you don't(portable system), go with 300W and add 2 more batteries but this is maybe more than you are willing to invest at this time.
The 12V compressor fridge is the largest single draw of electricity in our camper but we are 100% happy with its performance and would not go back to an absorption fridge.
Dave