Kohler SV600 Dies

I have a Kohler SV600 in a Cub Cadet and the engine will run for 30-45 minutes then start to die. If I pull the choke closed, it will barely keep running. I have rebuilt the carburetor, replaced the plug, fuel pump and filter. It almost seems temperature related. Has anyone experienced this? Any thoughts or ideas? I notice that the clear fuel filter looks almost empty (even when it is running well)

when it wants to die try loosening or taking the fuel tank cap off. and see if it returns to normal

check air filter, clean cooling fins under blower housing with shop vac, & clean underside of deck.