I have a hot water heater whose pilot light will not stay lit.

It has a history of not staying lit after weeks or months, but now I cannot get it to stay lit.

If I turn the dial to "pilot," light the pilot and hold down the red button for a minute, it will stay light when I let go of the button.

However, if I turn the dial from "Pilot" to "On" the pilot dims and goes out...

The water heater is a Rudd P30-6N, Natural Gas, 30 Gallon.

Any advice? I'm guessing that if it were merely the thermocouple, the pilot would not stay lit on "pilot."