Cover letter advice when re-applying for re-advertised role

Suppose someone made it to the final six applicants for a job with a national charity (and had a first interview) but didn't quite make it to the final two (who had a second interview) so obviously didn't get the job!

Suppose this applicant then got feedback to say that they hadn't sufficiently demonstrated a particular skill – but they knew that they had that skill, so resolved to demonstrate it better in future interviews.

Suppose they then saw that the role has been re-advertised, and they were keen to re-apply – better demonstrating that particular skill. (And it's definitely the exact same role, not just a similar position within the organisation.)

How should they address this in their cover letter when re-applying? 

Should they use much the same cover letter as before? (After all, it got them an interview last time!) Should they make sure to emphasise that skill in a slightly modified cover letter? Or should they rewrite it to say "look, I know you rejected me last time, but here's what you thought I was missing…"?

Or something else?

While the hiring manager may not be inclined to reconsider an unsuccessful applicant, the cost of re-applying is so minimal, there's really nothing to lose by doing so…