Common problems that affect the performance of gas stove pilot lights include clogging, a low flame setting or a faulty thermocouple. The fixing of these issues can be as simple as giving the pilot light a good cleaning or a total replacement of key parts.
Clogging occurs when ash, dirt or other debris gets lodged in the pilot light's burn area. It restricts the flow of the gas to the pilot light, resulting in a smaller flame, if it can be lit at all. The solution is a good cleaning.
If the pilot light has a low flame that is not caused by a clog, the setting may be off. A low flame setting can also cause the pilot light to go out from a sudden gush of air or even someone walking by. Most stove pilot lights have adjustment screws that govern the amount of gas flow. For this problem, it's best to check the appliance manual for the correct setting and the procedure for adjusting the flame.
The thermocouple measures the heat of the pilot light and then adjusts the amount of gas needed to maintain the flame. If the thermocouple isn't working, the pilot light tends to keep going out. Depending on the stove make and model, this may be a DIY project or require professional help.