Per this Q&A, creatures under the effects of spells or abilities that give them the frightened condition have that condition suspended while in a Paladin's Aura of Courage.
But if the spell/ability that frightened them gives opportunities for saving throws against that condition (e.g. at-end-of-turn, or once-out-of-sight-of-frightening-creature), do they still make those saving throws if the opportunities come up and the condition is suspended?
e.g. An enemy spellcaster casts Cause Fear on me, and I fail the save and am now frightened (but can make saves at the end of each of my turn to remove the effect). My party's Paladin comes within 10 ft of me, giving me immunity to frightened and so the condition is suspended.
A) Continue to make saves each turn to remove the effect even while in my Paladin's Aura?
B) Not make any saves while the condition is suspended, and if my Paladin moves away from me within the duration of the spell, become frightened again and only then start making saves against it?