To get the pivot point to stay at the changed position, you have to first set the pivot by right-clicking on the object when it is in the scene, then going to “Pivot → set pivot offset here”. To keep this as the pivot, and not have it reset, just right-click again on the object (with the new pivot point still showing on the object), then go to “Pivot → Set as pivot offset”. This should save the pivot location you chose even if you click off the object…