A gas fireplace pilot light may not stay lit due to several possible reasons. Firstly, it could be caused by a dirty or damaged thermocouple, which is a safety device that detects a flame and keeps the gas valve open. Secondly, a pilot light may go out if the gas valve itself is faulty or if there is a problem with the gas supply. Additionally, a clogged pilot tube or burner ports can disrupt the flow of gas and extinguish the flame. Other factors, such as a weak gas pressure or a malfunctioning gas regulator, can also prevent the pilot light from staying lit. It is crucial to have a professional inspect and repair the issue to ensure proper functioning and safety.