This problem been going on for 180,000 miles. Starter first replaced in warranty "Twice" under 20,000 miles at a Ford dealership. Ford dealership said there was nothing they could do after warranty was over. It still been happening for 12 years, every 10 to 50 times when started starter will not engage. Turn key on and off 2 or 3 times and it will finally engage. It been a nuisance That I've lived with for 180,000 miles. I know it will start but no one has an answer what to do to make it work correct every time. I've had independent garages look at it and replacing the starter was the only answer. What little item has everybody been missing?
The pinion gear on the starter meshes with the flywheel. I was taught in college that an engine tends to stop with the flywheel in approximately the same spot. I don't remember the whys of it. But at any rate you may have damaged teeth on the flywheel. Removing the inspection plate the teeth can be inspected while turning engine by hand.