Odds of Hanging On
First, let's talk about the demand for sports physicians' services. As long as a high school team still has a competitive athletic program, there should be a need for an advisory sports physician. On the college level, athletic directors have to juggle their program budgets to accommodate a bunch of team support services, including sports physicians' services.
Although teams will probably require a sports doc in some capacity, your role is, sadly, dependent on available funds. At the pro level, it might be a question of how much travel, intensity, and general work-related craziness you can stand. If you plan to stay on as a sports doc, you might want to stock up on your favorite energy products.