when u replaced the thermo coupling and re lit is the thermo coupling in the direct path of the flame
what do you mean it can cool down with a full burn and cause it to shut off , do you mean if it is a bad coupler and does it sound like i need to replace the water heater?
i am sorry you have two flames a pilot lite and a burner the pilot light remains on all the time but when the heater is on and heating the flame can loose contact with the thermo-coupling and it will cool down and cause it to shut off after heating the water up.
i dont think it is your gas control valve because you can get it to light just wont stay lit
As for the water heater being replaced that is a judgment question look at all connections and check for rust and corrosion.
The unit is only 7 years old no rust or corrosion. It seems the pilot light is not staying on,
When I get it lit it is a blue flame and the burner does go on.
Have a good night