ONE possibility, that is a K321 Kohler engine. In those engines, after a lot of operating hours, the HARD valve stems tend to wear a "pit" in the head of the valve adjusting screw. When you set the valves using a feeler gauge, the gauge "bridges" the "pit" in the head of the screw and you get a false reading... the valve is a LOT looser than is indicated by the feeler gauge.
ANOTHER possibility is that a tiny little spring has broken or fallen out of place on the Automatic Compression Release mechanism on the camshaft and levers and weight are rattling around.
Add those possibilities to everything else that can make noise in an IC engine!