It’s unlikely the valve clearance is causing that problem. How many hours are on the generator? The valve lash on your unit was to be checked after the first 50 hours, and every 500 hours after that.
If the generator engine is shutting itself off, it’s more likely that it’s due to low oil pressure or overheating. On your unit, the Low Oil Pressure and High Temperature Oil switches are out in the open, next to the oil filter.
Now, what I’d be doing is trying to determine if the engine oil pressure COULD be low, or the unit COULD be overheating. If the oil level is correct, the oil pressure is PROBABLY not low.
Checking for overheating is going to take a little more work. Are all the enclosure covers in place? Is anything blocking the airflow? This is an air cooled engine, and airflow is critical. The HTO switch closes at 293* F, and the normal running oil temperature inside an enclosure like yours is not far below that. It wouldn’t take much airflow blockage to make it run hotter. So check for dirt, debris, insulation, etc that could be blocking airflow. Both in and out of the enclosure.
Also, those switches CAN be faulty. I’ve owned at least three Generac units, and all of them use the same HTO switch, part # 094090, just like your unit. I have a new one in my garage now, because my home standby generator needed one a couple years ago. After determining the switch was faulty, when I removed it for replacement, it fell apart in my hands.
The Generac 3600 generator in my camper also needs its HTO switch replaced (same switch) because it was behaving very much like yours is. Unfortunately, I can’t get to mine without removing the generator from the camper, so that switch is unplugged until I get time to replace it.
In fact, both of those switches (LOP and HTO) can be unplugged for troubleshooting, as long as you understand what risk that exposes you to. On yours, I would probably rig up some alternate means of monitoring the temperature if I were going to unplug the HTO switch. And remember, on your unit, the enclosure covers need to be on for proper airflow.
:):)