Re: This'll never work
Of course, once they are out of earth orbit - and away from the cyclic gravitational pull of the moon, we have no idea how - or if - menstruation would work.
So in that sense, there's valuable science to be learned here.
My bet is that scientists will discover there's a weird backup system in place.
I would downvote you for casual stereotypical misogyny, but then your post did cause a scientific question, so I guess it's evens.