The problem is most noticeable when a PD weapon is chained to another main weapon e.g. or multi weapon turrets. As both are turning prediction is fluid, the weapon becomes indecisive and won't fire until it's too late.
A very slow turning main weapon won't changes. And naturally it gets worse when the missiles are already close.
So I suggest a more flexible prediction tolerance which is tight at long range and more lax at close range to adjust and account for the differing angular velocities of the target relative to the weapon.