SSDI denials happen frequently, with many of them focused around minor issues: Missing paperwork, a technical error, etc. Even so, these denials can take so long that some studies claim thousands of people pass away as they await their decisions. This happens each and every year.
Post-traumatic stress disorder (PTSD) is most common in those who have experienced trauma that is far outside of the norm. For instance, you may find it in soldiers who have been wounded in combat or police officers who have lost friends in the line of duty. While it's true that people can sometimes get it from car accidents and other such incidents, that does not happen as often.