Acrophobia, at present, cannot be cured. But, it can be treated. If you have the fear, you always have it although you may have it totally under control and may not notice it at all.
This is said to be true because people can relapse back into it, like drug addiction. Drug addiction can be treated but not cure. Once an addict, always an addict but, you can be in treatment and not acting on your problem. The same is true with acrophobia.