To the surprise of many runners, yes. Wearing an ankle brace has its benefits for the time being; however, over the course of time, the ankle region will begin to weaken. However, this is why many doctors or physical therapists will have runners perform different stretches and exercises that will help strengthen the muscles and ligaments in the ankle. Do keep in mind, if you only use an ankle brace for running, you should not notice any major negative changes like this.