Having an issue with my gas water heater pilot on my 11 year old 50 gallon Kenmore Power Miser 12 model 153.331544. Pilot always go out when burner shuts off. No issues with lighting the pilot. But I change temperature setting to hot, burner fires up, stays on for about 10 minutes, burner shuts off and pilot goes with it.....everytime.

The pilot lights with no problem and stays on all day with temperature setting on pilot lighting. I've removed the burner assembly and cleaned the thermocouple and pilot tube with sandpaper. Also vacuumed and dusted the inside of the chamber and the air intake screens below. Also checked mV from thermocouple after lighting pilot, got up to 22-23 mV.

Could I have a bad control valve? Or is there something else I should check? Control valve is about $110 so don't want to replace without a good feeling that this should be it.

Thanks for any help.