alopecia totalis in Down's Syndrome female

My 27 year old female Down's Syndrome patient had lost all the hair on her body. Now the groin and underarm hair as well as a bit of the eyebrows have grown back. The head has grown back a short pale nap that does not seem inclined to grow longer. Now we have one new dark hair on the top of the head, about 1/2 inch long. Several months ago there were three of these at the back of the head but they did not grown beyond one inch and eventually fell out. She is on thyroid medication that the MD insists is at the correct level for her. Loss of hair has been a problem off and one most of her life, however the hair had grown in and been stable for several years until about two years ago when it all fell out. She would love to have her hair back. We have tried many things with only as much progress as is indicated above. Does anyone have any suggestions?