Generators can run non stop for several days as long as it has enough oil and fuel to operate.
However if you have a portable generator it's best to shut it down after 14 hours or so to check the oil in it and give it 30 minute rest.
But I have run my portable generator with a larger tank attached for 3 days non stop and then shut it down for an hour while I checked the oil and allowed it to rest for a bit.
Then I started it back up and ran it another 3 days non stop.
When you need to run your generator to keep your refrigerator cold you should run the generator for at least an hour to keep the refrigerator cold every 4 hours.
As long as you keep the door closed on the refrigerator the refrigerator should stay cold enough for 4 hours.
So every 4 hours run the generator for at least an hour.
The refrigerator will usually come on for 20 to 30 minutes and then shut off for a bit and then come back on again.
If you can run a whole house generator or run a generator connected to your entire house then you could run the generator non stop.
This way the refrigerator and other appliances as well as lights will work.
I do this with a 7000 watt portable generator.
I have a separate breaker tied to the main panel outside and a plug on the outside of the house where I plug the generator into with a big 30 amp cord.
Then I can flip the other main breaker off and turn the generator plug breaker on to back feed the power into the house.
This way the incoming power from the meter is shut off so it does not back feed into the electrical grid.
Then I have my entire house powered and can watch TV, keep my refrigerator going, run my space heaters, computer etc.
I usually let it run all night so I always have power.