In the cooling mode for zone 1, why won't the temperature stay as set on the cool setting?

That would be a warranty issue, but wonder if you are reading set temperature, ambient temperature or 'set back' temperature? Contact the maker.

Comfort Zone Ceiling-Mounted 7500-Watt Fan-Forced ...

comfortzoneproducts.com https://www.comfortzoneproducts.com > products > ce...

MPN : CZ230ER. Warm up your garage, workshop, warehouse or event space with this powerful Comfort Zone Digital Fan-Forced Heater. Featuring a ceiling-mount ...

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Red for HOT, Blue for Cold, On for On, and Off for Off. Probably something that specifies the heat level.

'make model (what it is); would give a bit more context.

Or we can just GUESS!

Thermostat Modes/Settings Mean Explained

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Jul 19, 2021 - Heat is one of the classic thermostat modes found on just about every thermostat model. This mode allows you to control your heater or furnace.

What Do Different Thermostat Modes/Settings Mean?

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Probably the most crucial setting on your entire thermostat is the temperature setting. This setting allows you to pick the exact temperature you want your ...

What Do Different Thermostat Modes/Settings Mean?

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Nov 7, 2022 - The thermostat auto mode runs based on your desired temperature setting and the actual room temperature. Learn about thermostat settings.

What Do Thermostat Modes/Settings Mean?

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What is the best setting for your thermostat in the summer to maximize efficiency and coolness? When you're home, the recommended temperature is 78 degrees ..
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If your Comfort Zone CZ230ER is not cooling down to the setpoint and shutting off, there could be several potential issues causing this problem. Here are a few things to check:

1. Check the air filter: A dirty or clogged air filter can restrict airflow and cause the unit to overheat. Be sure to clean or replace the air filter as needed.
2. Check the thermostat: If the thermostat is faulty, it may not be accurately sensing the temperature in the room, which can prevent the unit from cycling properly. Try replacing the thermostat to see if that resolves the issue.
3. Check for leaks: If the refrigerant level is low due to a leak, the unit may not be able to cool properly. Have a professional inspect the unit for leaks and repair them as needed.
4. Check the compressor: If the compressor is faulty, it may not be able to properly circulate refrigerant through the system, which can prevent the unit from cooling. A professional will need to diagnose and repair any issues with the compressor.
5. Check the fan motor: If the fan motor is not functioning properly, it can prevent the unit from properly circulating air, which can cause it to overheat and shut off prematurely. Check to see if the fan is running smoothly and replace the motor if necessary.

If you are unsure how to perform any of these checks or repairs, it's best to consult a professional HVAC technician.

Try just using zone 1 for heat and cool..........

The thermostat is connected wrong.

Sounds to me like a bad damper or a bad zone panel. Turn tstat off and call for cooling on zone 2. Then see if your still getting cool air to zone 1.( where the main tstat is)

If you need further help, reach me via phone at https://www.6ya.com/expert/thomas_092728000e6acb79

Choose two colors of the thermostat wire, and connect them to the NO and COM and connect them to the zone control board leads for the zone intended. Almost all zone valves spring return open when deenergized. So ensure the zone valve is open with the system is off. At the base of zone valve there is a set screw that needs to engage the damper valve shaft in the open position with the motor in the spring release position. Most zone valve are 90 degree moment from full open to full shut. If you have a Carrier zone valve, they go full open to full shut in 45 degrees of motion. Your open stop need to be set so the valve stops in the full stop position.
To help understand the operation of a zone system, say you have 2 zone system and zone 1 thermostat initiates a heat or cool demand. Zone 2 valves energizes and shuts and zone 1 stays open and allow air to heat/ cool zone 1. If zone 2 thermostat simultaniously initiates the same heat/cool demand, the zone 2 valve opens and both zone heat/cool. When either thermostat is satisfied the opposite zone valve closes and when both thermostat are satisfied both zone valves open.
Hope this helps you understand zone operation. The same works for higher multizone systems.

The stat that works is called the main and the other two are called slave stats. The stats must be set to heat or cool the same as the main. If you want one room to cool and one to heat , sorry. Need to upgrade to auto changeover. Is this AC actally a Heat pump?

Verify 24 volts at the low voltage transformer inside the air handler. If it is OK, jump out the red/green and yellow thermostat wires. If everything comes on, replace the thermostat.

the multiple zone thermostat should work fine but sounds like this one has an internal failure try replacing the thermostat