EDICT : sousha +(PC) ;-)

The current entry is 'suffering' from a lack of PC.

壮者 【そうしゃ】 (n) man in prime 

Not to mention from a lack of second person possessive pronoun.

"person in his or her prime" would appear to be the opinion of the largest faction of the usage panel opinion as related at dictionary.com
with "person in his prime" and "person in prime" trailing behind.

No doubt if I said I preferred "person in their prime" I'd be buried under a heap of grammar books, even though it is as common as "person in his prime" as far as Google is concerned.

Anyway as "man in _his_ prime" is a well known common phrase I think it is worth keeping _as well as_ a separate more inclusive version.

壮者 【そうしゃ】 (n) person in his or her prime; man in his prime

For what it's worth it was used with reference to a woman in the book I was reading.
.