If you fail a save from a Pit Fiend's Fear Aura, you are Frightened
Yes, you have to make a save against each individual creature that has the fear aura.
No being immune to one fear aura does not make you immune to the other fear auras.
However.. If you look at the description of Frightened, you will see that the effects do not stack. If you have ...
The Pit Fiend’s fear aura ability reads:
If a creature's saving throw is successful, the creature is immune to the pit fiend's Fear Aura for the next 24 hours.
You would only be immune to the particular pit fiend’s ability. An ability explicitly states if saving against it immunizes you against the same ability from all creatures of that type. For example, ...