Why did the population tend to return to a stable state of about 40 buffalo in many different situations?

Because if you had more room, the buffalo can roam around more for food and space so more can be produced.

you did not attach the discourse, but i assume it to be the discourse on the origin and basis of inequality among men (the original titile in french is: "discours sur l'origine et les fondements de l'inégalité parmi les hommes"), also know as "second discourse". in this discourse, jean-jacques rousseau emphasizes that private property is the basis of all inequalities.

therefore, what enabled the old regime to maintain as long as it did was private property.