Perianal fistulas are actually thought to be an immune-related skin problem. Many times these dogs have allergies, oftentimes to food, and cyclosporine can stop the immune system from reacting and attacking the skin and surrounding tissue. Once the body/skin stops reacting to the immune stimulus, the fistula will start to heal up.
If the Atopica doesn't help, I have also had some success with tacrolimus. I also have changed the diets on my patients to Prescription Diet Z/D--I have been able to take a couple dogs of the drugs completely once they were on the new food for about 3 months.
Good luck--it is often a difficult disease to treat and manage.