Can someone retake a denied medical?
This is my personal experience having nearly lost my medical: If you are in the U.S., you will have to check the box on the application stating that your medical has been denied in the past. You will have to check that box every time you apply in the future. Having nearly had my medical denied in the past, my advice is to 1) find the most senior AME in your area and schedule an appointment for consultation. Explain your situation and take his/her advice. 2) Follow through on that advice (I had to see a well-regarded neurologist for a few hours' worth of exams and interrogation). Bring those results/reports with you to your next AME visit and have him/her send them to the FAA with your next medical application. The FAA's medical office in Oklahoma City will review your case and most likely send you a letter. I was able to get a medical issued the day I applied, however, the letter I received from OK City put me on a six month schedule before the age of 40. I strongly urge you to consult with the most senior AME you can find. 

tl;dr - If you have been previously denied. You will have to provide documentation to your AME to overturn the denial. 

Caveat: I am only familiar with the U.S./FAA system as a pilot.

[ I'll try to tidy this up when I get home later today ]