It wasn't until I resigned my seventh job (with Accenture) because of their refusal to let me work from home that I saw a psychiatrist. Everything fell into place.
Why do employers still refuse to let me work for them from home?
You are probably choosing the wrong employers, and are getting hired with the wrong expectations.
Apparently, you chose an employer, worked there, and only then decided they should let you work from home. When they didn't you quit. Only you and the company can know for sure why they refused. Perhaps they didn't trust you enough to work remotely. Perhaps their infrastructure or work policies aren't sufficiently developed to permit remote work. Perhaps your role requires your physical presence more than you perceive. Perhaps they just didn't like you enough.
Instead, seek an employer with the specific intent of working from home. Many employers boast flexible work arrangements or work-from-home jobs on their websites these days. As @Shauna adds there are also sites dedicated to remote job postings now, such as weworkremotely.com. Find one of those companies. And during the interview process make sure to specifically ask how it works at their company, and learn if it fits your needs or not.
You can't just go to a company, get yourself hired, and then decide that they should let you work from home. It simply doesn't work that way.