AC Question
 

From time to time the AC will shut off on its own, the "cool on" will flash on the thermostat

Any suggestions?

What brand AC and what brand thermostat, we have carrier AC and Carrier thermostat and have never seen the condition you describe.
Does the AC come back on after a little while? Have you changed air filters? Is this a new error? How old is the AC unit? There may be a thermal overload on the motor which may automatically reset, but without additional information it will be hard to provide any additional info.

When you say the AC shuts off, are both the inside unit (fan) and the outside unit off?

The symptoms I had were the thermostat showed cool on, the outside unit was running, and the inside unit seemed to be off but was running very slowly. I needed a new electronic module on the fan motor.

You said the cool on was flashing. What does the manual say about that?

EDIT: There is an explanation and some things to try at this link.

Could your drainage sensor be malfunctioning by shutdown and starting up again?

Clogged condensation line- flushed and fixed

Hire a professional? Get it diagnosed?

Thanks for passing that along. Hopefully, one of the suggestions helped you find that two days ago.