Aura of Cowardice

[legomaster00156]

At 3rd level, an antipaladin radiates a palpably daunting aura that causes all enemies within 10 feet to take a –4 penalty on saving throws against fear effects. Creatures that are normally immune to fear lose that immunity while within 10 feet of an antipaladin with this ability. This ability functions only while the antipaladin remains conscious, not if he is unconscious or dead.
If a creature normally immune to fear is struck by the frightened/panicked conditions, and leaves the radius of this aura as a result, do they cease to be afraid?

[Particle_Man]

I would say yes but then then they get scared again if within 10’ again.