Fain/Mordeth is unique to this Age so he will come back for each third Age but will not appear in the others. It make sense to me since he's a "consequence" of the appearence of the Dark Lord in the previous Age.
It could be like that (or not at all ;-)
Age 4 : humans rediscover science and live like us
Age 5 : humans travel to other worlds / create marvelous things and terrific weapons / destroy the universe(s) (Big Bang)
Age 6 : (re)creation of the universe(s)
Age 7 : Dinausors and etc.
Age 1 ...