I've never heard of periods ceasing due to a lack of red meat, though yes, I'd imagine that would be a great incentive.

Only that among women in my close proximity (close enough that I could glean their cycles) that a lot of them would have ferocious meat cravings once a month that enabled my own red meat habits, so that even when beef prices jumped, and we had economic reasons to cut down, meat would be on the menu again.