Fear of heights, also known as acrophobia, is a specific phobia. Specific phobias last a long time, and the average duration of illness is 20 years. Your fear of heights will wax and wane (get better and get worse) throughout the time you have this anxiety disorder. If you don't treat the acrophobia with exposure therapy, then your fear of heights continues and may even worsen, especially if you engage in avoidant behaviors (where you avoid the feared stimulus).