Not sure if this applies at all but for what it is worth. I used to be in charge of an ultra pure water system. The water had to be kept moving at a a pretty good speed to prevent bacteria from growing. Even then we did bacteria tests and sanitized the system once a year.
Also we drink a lot of bottled water, and if we open a bottle and take a drink and then forget about it, WOW can it smell bad in about week. Bottled water is DI water with some minerals added for taste.
So I think RO/DI water could sit for awhile, but not indefinitely.
Sorry if I confused y'all.
Scott