The stockpile is limited by the number of storage facilities you build, plus 50k as a starting amount. Everything above that spoils away.
Note:
Storage facilities do not need a spaceport.
Although you do need some storage facilities to handle massive retrofits and other fluctuations in usage rates, each storage facility is taking up a slot which could be producing minerals, research or other valuable things.
PS:
To see your current limits, look on the budget screen at the very bottom.
Ah, well that makes clear the need for harmony! And the cultural traits? Ought my drearily predictable minmax be scientists, or Berzerkers? Or at least, which bonuses/maluses are or aren't working?