The fear of heights is a type of anxiety called specific phobia. The fear of heights can last several years, and even decades. The good news is that if you develop a fear of heights in childhood or early adolescent years, then 50% of those with a fear of heights will not have it anymore within 5 years (Carandang, 2014).
Reference:
“Chapter 3 – Specific Phobia.” Anxiety Protocol. Carandang C. 2014. Healthy Mind Research Corporation.