Three things can cycle it off. In the case of a COLEMAN with "Local" (not a wall mount thermostat) there is one more.. And I'm suspecting that last one.
If your controls are knobs on the ceiling in roughly the middle of the grill....
Remove the knobs. tehn teh grill and filter
There si a small "Tube" with a bulb on the end
ON my Carrier's this was the frost sensor and it was stuck in the evaporator coils but on a COLEMAN with ceiling controls THIS SENSOR DOES NOT EXIST
The sensor that LOOKS LIKE IT. it the room air temp sensor and is NOT supposed to be poked into the condenser.. It's just supposed to hang there in free space. Why they did it that way I do not know and I can see several "issues" with doing it that way Find a place you can zip tie it down and be happy.
THIS ONLY APPLIES TO CEILING CONTROLLED UNITS. If you have a wall-T-Stat this does not, far as I know, apply.