Hi Dirk, that's a really good question and doing a cursory from my end yields nothing conclusive reach leaching. However, I found these helpful bits:
It might be better to store distilled water in glass, but the glass must be sanitized
If storing distilled water in its original plastic jug, store it sealed tightly in a cool, dark place
If you're really concerned, there are home water distilling appliances under $100 that might do the job straight off your tap.
Best, Tamara, SleepApnea.Sleep-Disorders.net community advocate