Balance training is a supremely low-tech but increasingly well-documented approach to dealing with unstable ankles.
Here's the key paragraph in the article:
Why should balance training prevent ankle sprains? The reasons are both obvious and quite subtle. Until recently, clinicians thought that ankle sprains were primarily a matter of overstretched, traumatized ligaments. Tape or brace the joint, relieve pressure on the sore tissue, and a person should heal fully, they thought. But that approach ignored the role of the central nervous system, which is intimately tied in to every joint. “There are neural receptors in ligaments,” says Jay Hertel, an associate professor of kinesiology at the University of Virginia and an expert on the ankle. When you damage the ligament, “you damage the neuro-receptors as well. Your brain no longer receives reliable signals” from the ankle about how your ankle and foot are positioned in relation to the ground. Your proprioception — your sense of your body’s position in space — is impaired. You’re less stable and more prone to falling over and re-injuring yourself.
It's all about the nervous system and central integration. The human body is a receptor based system. Information is received from sensory stimulii which includes balance and sense of position in space. That information is sent to the CNS, the spinal cord and brain, for processing and motor output. With less or aberrant info coming in there will be less or aberrant info going back to organs, joints, and other body structures. Weakness and instability will lead to more weakness and instability as the body tries to compensate in order to maintain balance both structurally and functionally. Professor Hertel mentions ligamentous receptors but there are also receptors worth mentioning in the joints and muscles. The excercises he reccomends are very advanced and at the same time relatively low tech. They demonstrate a real understanding of anatomy, physiology, and neurology.