A monopsony comes to exist largely for the same reasons that a monopoly comes to exist. That is, monopsonies can evolve and continue to exist if very high barriers to entry exist. In other words, if it is very hard for any other buyer to enter the market, there can be a monopsony.
Let us look at two kinds of barriers to entry. First, there can be very high start up costs to enter a market. An example of this could be the National Basketball Association (NBA) in the United States. It would cost a tremendous amount of money to create a full-fledged new basketball league that could compete with the NBA. Therefore, there are no competitors to this league in the United States. Since no other league in the world has as high a level of play or of wages, almost everyone who is able to will want to play in the NBA. This gives it a monopsony. Second, there can be one company that owns all the resources in a given area. This was more common a long time ago. For example, if there was a town whose only real resource was a coal mine, the owner of that mine owned all the resources in that area. It was not possible to build another mine and there were often very few other good choices for employment. Thus, the coal mine was the only major buyer of labor in that area.
Thus, monopsonies can evolve and persist if there are major barriers to entry into a market.