A residential customer calls to report that the furnace stopped in the middle of the night. The furnace is old and has a thermocouple for the safety pilot. The technician arrives and goes directly to the thermostat. The thermostat is set correctly for heating, but the thermometer shows a full 10°F below the thermostat setting. This unit has air conditioning, so the technician turns the fan switch to ON to see if the indoor fan will start; it does. The furnace is in an upstairs closet. The technician sees that the pilot light is not burning. This system has 100% shut-off, so there is no gas to the pilot unless the thermocouple holds the pilot-valve solenoid open. The technician positions the main gas valve to the PILOT position and presses the red button to allow gas to the pilot light. The pilot light burns when a lit match on an extender is placed next to it. The technician then holds the red button down for 30 seconds and slowly releases it. The pilot light goes out. What is the likely problem and the recommended solution?