Engine runs for short period and cuts out.

Do the engine rpms drop or only the blade speed?

If belt is tight at cutting height and engine rpms hold, then the vbelt from engine to deck is likely is dry burnished or oily.

First check the blades are install cutting edge down (fin up). If belt from engine to deck has a glassy finish (burnished) replace belt or remove burnish with sandpaper.

It appears be relatively complicated deck system. See owners manual regarding deck remove/install.

https://www.manualslib.com/manual/1205115/Honda-Hf2622.html?page=20

The OHV engine requires periodic valve adjustment. Typically every 300 hrs.

Another possible cause is an ignition module failing at operating temperature. Run until it fails and check for spark at BOTH plugs.

It is like you overworked it and it got some efficiency fault.Kindly see a dealer closer to you.

They will run until the air pressure is at the max, then will shut off. This is normal. When you use the air & it goes below a certain level, the motor should run again. If the pressure is not reaching the max value, then the motor may be overheating.

Sounds like a fuel cut out switch!

Maybe some thing in the Carburetor or plugged fuel line? Worth a check

I heave the same problem on my Corsa B 1.0 2000, engine cuts out, and whe it happens, I hear one of the relay under the right side of the dash buzzing. After a couple of minutes, starts like nothing happend.
So far I manage to find that the speed sensor is faulty, when I tap him the car stops. I order a brand new one, but I'm not sure that was the issue.
I order also a Opel Tech2 tester from ebay and it has to arrive next week, then I can see the error code.

You may have a small air leak at the carb, sometimes found at the bulb primer. This allows the engine to stop picking up fuel due to sucking air into the fuel line. If you re-prime, it will run again for a short period?

Are you topping off the gas tank (MAX OUT) while you're filling?

The emission control system can soak with gasoline if you over fill the tank.

Locate the emission line that lead to the charcoal canister and let it air out under direct sunlight.

After 1-2 hours,reconnect the line and use starting fluid to start the car.

After 10 minutes of warm up time,then take it for a short test drive.

If the engine dies shortly after start. Squeeze the spray wand trigger to release pressure on the unit. When restarting let the engine run for a few min(2-3 no more) to warm up, the unloader valve on the pump should keep pressure to a minimum. If the engine stalls or will not run you need to check your carburetor and clean it. BECAREFUL as FUEL is FLAMMABLE and there are small parts in the carb float bowl that like to get lost. A rebuild kit for most carbs is less than $8USD and a can of spray carb cleaner about$2-3. Install a fuel cut off valve($6) to keep the carb from gumming up again. Shut off the fuel when not in use or for periods of prolonged storage. Take a picture of the carb on the engine(my memory is bad) and during disassembly to assure you get it back together properly. The idle screw should be turned in(to the right)till it seats lightly then backed out 1&1/2 to 2&1/2 turns to start with. After starting the engine adjust for good idle and running buy turning in or out to attain the best idle. If this is helpful, Please leave Feedback. Thanks, SnugglePants