How often are you bathing her? Persians are notorious for getting grease build up in their coats if not properly cared for and needing diligent grooming routines. I have only short hair cats because cat grooming is one of those far off concepts for me (even when it comes to myself it is a good morning if I don't run out of the house with my hair still wet ) Here are some links to more information that may be helpful:
It might be that she wasn’t rinsed well enough. When I started out, my girl would dunk her face and chest in the water after a bath. The breeder told me to rinse her longer - it worked.