So I believe that the Ministry's stockpile of Veritaserum under a stasis charm would be very sizable and I believe they would have enough to, at minimum, dose hundreds of people.

On the other hand, the ministry could very well limit its stockpile due to its power. Imagine how much damage a minister could do by dosing the 100 most wealthy and influential people of magical Britain to get all their secrets. I don't think pure blood wizards would risk that happen. (hell, maybe something like this already happend in the past, resulting in some sort of limit?)

Considering this, you could say the ministry has 3 vials in case of emergency. Enough to use in life or death situations The Aurors spoiler but not enough to ever use in day to day operations of the ministry.

Then its just a matter of somehow getting rid of this small stockpile (sabotage, ingredient scarcity, ministry incompetence?).

A possible reason in the case of The Aurors: spoilers

I can understand the reluctance of using Veratiserum, especially since "the aurors" is a great story and having it used would hurt it. But not mentioning it at all made the ministry, harry included, look a bit incompetent since the outcome could have been improved if someone just remembered it existed.