I think the aeon can only be in one place at any time (one fayth).

Pain in the butt if you've just climbed Gagazet to fight you-know-who, fancy summoning Ifrit for a nice 9,999 hit and... nope, nothing. Meanwhile, Issaru is just visiting Kilika and is using Ifrit to have a nice barbeque on the beach...

This never happens though. Would be interesting if occasionally you couldn't summon an aeon for a while because it's in use elsewhere...