Looking for a new battery

[Outdoordog]

My current battery (jackery 500) will shut off if it doesn't send out more than 10 watts for a few hours, my fridge can drop to 1 watt for hours, hence the battery shutting off.
Is there a battery that will keep my fridge on indefinitely?

 

[SJ.Overland]

I don't know about other manufacturers but ECOFLOW power banks have the ability to specify the auto-shutoff time period. Might be best to reach out to each OEM/Retailer on how their auto-shutoff works before purchasing.