Kohler cv491 why does this happen. cranks and runs good 5 to 10 min. goes dead must sit approx. one hour then cranks and same thing?

When you say it "goes dead" do you mean it dies and won't start (even though it turns over) or nothing happens when you turn the key, not even a click?

Check your fuel filter. Is it dry? Mine was and found the vent in the fuel cap was plugged and it didn't allow fuel to flow through the filter to the carb