The Miata fuel system is simple and durable: an in-tank electric pump, a filter, four injectors, and a vacuum-referenced pressure regulator. Failures are uncommon and easy to trace.
Fuel pump: - Symptoms of a failing pump - long cranking, hot-start hesitation, cutting out under load, or a no-start with the pump silent at key-on. You should hear a brief pump prime when the key goes to ON. - Testing - listen for the prime, check fuel pressure at the rail, and verify the pump relay and the AFM fuel-pump switch (1.6) or ECU control. There is a diagnostic connector to jumper the pump on for testing. - Replacement - the pump lives in the tank, accessed through the sender; a reliable OEM-quality unit is worth it over a cheap generic.
Fuel filter: - Change it - a neglected filter starves the pump and mimics a weak pump. Location varies by year (engine bay or under the car).
Injectors: - Rarely fail - clogging is uncommon on a running car; a genuinely dead or dribbling injector shows as a cylinder-specific misfire or a fuel smell. - Cleaning - a bottle of good injector cleaner handles minor deposits; ultrasonic cleaning restores neglected sets. Match injector size when upgrading for boost.
Pressure regulator: - Vacuum-referenced - a torn diaphragm leaks fuel into the vacuum line (you will smell fuel and run rich). Check the vacuum nipple for wet fuel.
Keep the filter fresh and the pump original-quality and the fuel system will outlast most of the car.