When you choose a target for a special ability that target cannot change.
If a special ability is prevented, and the prevent is later negated, then you can select a target for the ability. It never targeted in the first place, so there is no change in targets.
If a dominant is played that was intended to target a certain card, it may be picked up if the intended target is no longer available due to the effect of another card. It never made the actual targeting, since the target was never really available. So, there is no true change of targets.
If a non-dominant ability is activated and an available, legal target is selected, then that target cannot change. If the ability is interrupted, and the target is removed, then a second target cannot be selected.