Just came across this article which seems to suggest that Prince Harry maybe going bald also like his brother Prince William,
To be fair, none of the pictures were clear, it could very well be the lighting that makes his hair look worse than it really is.
I believe he is in his 30s, the odds are probably in his favor given that he still has a good head of hair; there are plenty of treatments out there that may help slow down the progression for his case.