In Supernatural, they have a tendency to try to keep as close to the real world's mythology as possible, inventing only when necessary to flesh out missing details. As such, I think it's appropriate to answer this based on those religious practices relevant to "holy water". Many religions bless water, but the Catholic religion is perhaps the most relevant here. Wikipedia explains it best:
In Catholicism, holy water, as well as water used during the washing of the priest's hands at mass, is not allowed to be disposed of in regular plumbing. Roman Catholic churches will usually have a special basin (a Sacrarium) that leads directly into the ground for the purpose of proper disposal. A hinged lid is kept over the holy water basin to distinguish it from a regular sink basin, which is often just beside it. Items that contain holy water are separated, drained of the holy water, and then washed in a regular manner in the adjacent sink.
I am not an expert on the Catholic faith, but it can safely be assumed that if holy water were disposed of in regular plumbing, rather than the plumbing becoming blessed it would defile the water and remove any special properties it once had.
I think this is also the key to storage: anything that would defile the holy water would render is unspecial. The best I can come up with on that point is the following:
defilement
The condition of uncleanness. In biblical and ecclesiastical usage it means to render unclean by contact with unclean things, by eating forbidden foods, by polluting sexually through adultery. Its most important meaning is to be stained with sin.
It's unlikely you'll mix bacon in with the holy water, so that can can be ruled out. Similarly, it's not a person and so can't be adulterous. Mostly we're looking at contact with unclean things (in the religious sense, soil isn't necessarily bad).
Interestingly, it may be true that flowing water is already considered holy even without a blessing. John the Baptist after all performed baptisms in the river, and additionally rivers and streams were in some mythologies impenetrable barriers to vampires and such.