[Golfer222]

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

Any suggestions?

[villagetinker]

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.

[Bill14564]

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.

[Keefelane66]

Originally Posted by Golfer222

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

Any suggestions?

7 Reasons Why Honeywell Thermostat Cool On Flashing - Google Search

[Michael G.]

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

[Golfer222]

Clogged condensation line- flushed and fixed

[mrf0151]

Hire a professional? Get it diagnosed?

[Bill14564]

Originally Posted by Golfer222

Clogged condensation line- flushed and fixed

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