I too have recently re-watched the whole series as well as the film, and would like to know: Where was it ever established that the Reavers "don't reproduce naturally"? I sure don't remember anything remotely like that being said, or even implied, by anything on-screen.
I'd sat that devoid of the usual social restraints, and driven almost entirely by their more animalistic urges, I'd think they'd breed like rabbits.