Stockpiles won't be moved through trade routes, only production. The amount of resources to be moved takes time to calculate and will change each minute(watch) until it hits an equilibrium. You can move stockpiles manually, though that can cause issues.
A large number of things you do take time to take effect. The biggest one that isn't exactly obvious is efficiency on planets. This changes the production output of the available workforce. This takes a big drop each time a planet is conquered, it's designation is changed or a negative event (low supplies, low happiness, revolt, civil war). A planet regains efficiency over time.
A high tech, un-inhabitable world with low efficiency can become a uncontrollable location for a long time as it gets stuck in a loop of civil wars when ever a player controls it. This happens when a world has such a low efficiency, and to high of a static tech level and (even with imported resources) it dosen't meet it's need for life support items because it didn't calculate in the lower efficiency for the automated assignment of the production of life support materials. Which causes negative events that lower efficiency that isn't calculated for when auto assigning work for life support items which yadda yadda yaddas.
This also can be caused by teching up a world prematurely, though these self right a little better as they drop in tech after they civil war into independence. Which means they'll stop having issues because they won't demand things they can't supply.