ummm i've always been on the fence concerning distilled water. And there was someone on this forum awhile back who had fasted and had problems with hair falling out, but not sure if she was drinking distilled water or not, yet as Fonty says, many people fast for weeks and don't have a problem.
I think i would use it for fasting but not normal everyday use. As you say hard to get hold of here anyway. I've not used it on my short fasts so far though. If mineral water is so bad for you, how comes you hear of tribes, civilizations and people drinking spa/spring water and getting great health benefits. For detoxing maybe but i'm not convinced you need it all the time.
My hair is my crowning glory, i would be mortified if it started falling out.