In my experience most grow out of it, especially if he has never been hit hard by a ball. That being said, one way that you can "desensitize" him is it throw tennis balls for him to hit. Work with him on seeing the ball, that way he will know better which one is or isn't going to hit him. If he can concentrate more on the location and proper swing, the less he'll feel threatened by each pitch.
Also, work on the proper way to turn when a pitch IS going to hit you. (for some unknown reason, some kids turn TO the pitcher when they need to turn away, tuck thier necks to their shoulders, etc.)
As he continue to play, inevitably he WILL get hit by the ball when fielding in practice or a game. I ALWAYS go to the player and say, "Did that hurt?", They sometimes are stung a bit, but most say "No" and I'll reinforce the fact that it may hurt for a second, but it goes away really fast. Thay usualy agree and lose the fear as time goes on.
Also, like you said, as the oitchers get better, they won't hit many if any during a game. You may want to get him to count how many per game and let him understand that it doesn't happen ALL that often at any age.

Hope that helps.

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