Actually, the RAW are quite clear - if one remembers that rules in 5e are either fluff (simply to show intention, I suppose) or a direct statement invoking game mechanics.
"...you and friendly creatures within 10 feet of you can't be frightened while you are conscious."
This is clearly not the former, so must be taken as statement invoking game mechanics. The only direct game-mechanics relevancy of the word "frightened" is the condition called "frightened". It can not refer to the event of acquiring the frightened condition because it does not say "...can't acquire the frightened condition...", nor "...can't become frightened...". It says "be", not "become". Thus, view it like this:
if { distance(X.pos(), Paladin_A.pos()) <= 10' && status(X,Paladin_A) >= FRIENDLY && Paladin_A.condition.conscious() && Paladin_A.level() >= 10 } {
if { X.condition.frightened() } {
X.condition.frightened(NOT);
}
}
Clearly, beyond any doubt, it is impossible for friendly creatures in the aura of courage to have the frightened condition. There is no ambiguity here. However, once they leave the aura, can the frightened condition return? It certainly could - the Aura rules do not say it can not. That becomes up to the DM.