The answer to 'why is my recessed lighting outlet not working' is that there are several common causes, including a tripped circuit breaker, a faulty light fixture, or a problem with the wiring. Recessed lighting outlets can stop working for a variety of reasons, but the most frequent issues are related to the electrical supply or the light fixture itself.
If the outlet is not working, first check the circuit breaker to see if it has tripped. Reset the breaker and see if that restores power to the outlet. If the breaker keeps tripping, there may be an electrical short or overload in the circuit. This is a job for a professional electrician, as they can safely diagnose and repair the issue.