2003 Mazda Protege Vehicle Won't Start

2003 Mazda Protégé 5. 72,000 miles. For the last few years I’ve had an intermittent issue with the vehicle not starting. Driving under different conditions, various distances, I will park the car for a short period of time, then go to start it again only to get battery power but no engine. No cranking or clicking noises, just silence. Then anywhere from an hour to a day later, after various tries with the same result, it will start up again like new and drive for days or months until the next reoccurrence. I’ve had two Mazda dealerships look at it (including when it was under warrantee) and several mechanics, but no one can pinpoint the problem. Would greatly appreciate any ideas.