I, my wife and my first born experienced drinking distilled water long term (12 months) and in our observation, this is one of the contributors that made us sickly.
We live in Manila, Philippines and the brand we used for 12 months were: Absolute and Wilkins.
We switched to Hidden Springs (natural spring water from the mountain of mt. Makiling) and our we had better health from then on.
This happened around 2001 to 2002.
Note: I have never tried distilling water at home yet.
Note 2: At that time, we were still western medically brainwashed and S.A.D. brainwashed at that time.