Three suggestions:
1. Make sure he has the right sized hat. Too large and it falls off. Too small and it is never really on in the first place. (So, getting a tighter hat won't work.)
2. Show him how to put his hat on properly. Too many kids just throw it on top of their head, leaving their bangs coming out in front. That makes the hat slip off easily. The proper way to put on a hat is to put the front of the inner band against your forehead, then pull it down over your head from front to rear. The top mop then weighs against the front headband and actually holds the hat down.
3. Ever video him with a slo-mo feature? If frame-by-frame shows his head jerking downward or off to the side, part of his problem may be in his mechanics. Head should remain upright, nose to the plate. No head jerking.