Hello,
What your son seems to be having is alopecia aereta of scalp and eyebrows. It is an autoimmune disease characterized by unpredictable, nonscarring hair loss of the eyelashes and eyebrows. In such cases, to promote growth of eyebrows, just eat a healthy protein rich diet and take some multivitamin supplements for some days. The most important nutrients are biotin, silica, magnesium, sulfur, zinc, and vitamin B6.