The most common cause for a furnace pilot light to repeatedly go out is a broken thermocouple. The thermocouple controls the pilot light, so if it is damaged or needs cleaning, it can cause the pilot light to malfunction. Thermocouples are easy to replace yourself; they can be purchased at local hardware and home improvement stores.
To replace the thermocouple, unscrew the internal connecting nut and copper lead that are located inside the gas line connection. A mounting bracket is located underneath the thermocouple tube. Unscrew that bracket nut, and replace the thermocouple.
In addition to a malfunctioning thermocouple, issues with the pilot light are also caused by obstructions, a low flow setting on the pilot light line or a dirty pilot light line. The gas flow to the pilot light can be easily adjusted to a higher setting. To clean a dirty or clogged pilot light line, all equipment must be completely disabled and cooled down. Once the system is cooled, remove the nuts, bolts and thermocouple tube. Take a wire brush, and gently scrape away the soot and dirt. Once the area is free of debris, replace the tube and tightly screw the nuts and bolts back into place. If troubleshooting does not work and the pilot light continues to malfunction, contact a professional for further assessment.