Soooo, if he does it again what happens? They'll fire him?
"Right thats it. Hand in your crown lad, you're finished. From now on you're working for a living.
Jenkins! Escort this 'commoner' to the rear entrance please."
His position in the line of succession is by virtue of his birth, and his birth alone. Technically, a reigning monarch can remove people from their line of succession. But that is so unlikely to happen to Harry it's barely worth mentioning.
His actual job, however, is dependent on performance and merit (one would hope) as it is any other officer of the British Army.