According to Dr. Mercola hair loss is a result of the lack of minerals. He recommends not to drink distilled water.
I have to question the distilled water advice. It would seem to me that as long as you get the necessary amount of minerals, how can distilled water wash them out of your body? I can see why you shouldn't take distilled water when you are fasting. Doesn't water get mixed up with whatever is in your stomach?