Sounds like you need to replace the thermocouple, it looks like a piece of thin copper pipe and is in the flame of the pilot light. Sometimes, removing it and cleaning the connection (where it fixes into the control box) with a pencil eraser will sort it. Make sure it is in the flame when you refit it. It is a safety device, designed to cut the gas if the flame goes out.
Pete.. service engineer (oilysump@aol.com)
Pete, November 2006