I'm wondering... If you use use the barrel of chest every day then does it become a safe place to store things? In my experience that is exactly what happens.
They reset every X amount of days that they go untouched*. X is something like 7+ I believe. And as far as I know this also applies to plants, which is why the Lavender in Whiterun never seems to respawn for me.
*It's really more of a "every day they aren't loaded" so the barrels in Whiterun shouldn't reset if you visit Whiterun at least once per in-game week.