I am going to keep an open mind about this (as I do about many things), as nothing is more valuable than personal experience. This article is interesting, called "Why I say no to distilled water only". Somewhat controversial I am sure, but here's a quote:
"It's amazing to me how blindly most health seekers follow the advice of the above three gurus as well as the advice of modern health writers who use Bragg, Walker, and Shelton as their main sources of truth"
and specifically relating to your experiences:
"I opened my eyes because about two years ago I started hearing from long-term distilled water drinkers who had been consuming only distilled water and who had developed troubles with their hair either thinning or falling out in clumps. I've subsequently learned that hair loss is a condition often associated with various mineral deficiencies."
But he does also say:
"Let me say here that I still consider distilled water the water of choice when detoxing or working to heal a serious health challenge"
I drink tap water anyway, because distilled is hard to get and expensive where I am. If ever I do use distilled water for any length of time I will take the usual precautions as I did on my first fast, i.e. monitor myself very carefully.