My stop/start function, works sometimes, is there a separate battery for this problem, it started after I had the car for at least a month
Stop / Start does not work all the time . There are certain things that will cause it to keep the engine running . As for the battery your owners manual should answer that .
Do a web search for start/stop and you will know more about it.
Some start/stop systems are sensitive to the condition of the battery. If your vehicle has the original battery from 2016, it is overdue for replacement.
No there isn’t a separate battery.
Stop start doesn’t always work all the time. If the car’s battery is getting a bit old, the computer will prevent stop/start.
In addition to the other valid comments, I want to add that the auto stop/start feature will usually not function until the engine warms-up fully. If the OP lives in an area with cold winter conditions, this is a factor for him to be aware of.
Using a web search seems to show that 2016 and up Jeep Cherokee with stop/start has 2 batteries .