The Nerevarine managed to become immortal through surving the side effects of corpus - she/he became a super soldier (or mage) basicaly.
The CoC managed to become immortal through mantling Sheogorath.
In Daggerfall,the Hero had the Totem of Tiber Septim and,while he could choose to use the Numidium to fight people,he could make the King of Worms immortal.But,surely he could make him/herself immortal?And why not,he certainly earned it after what he did.Was the Warp in the West caused by the player?
In Arena,the staff of Jagar Tharn was very powerful,made of the essence of Tamriel itself I believe.Nothing said Jagar Tharn was immortal,but why keep the pieces in Tamriel?It may be indestructibe,but surely you could have cast the pieces into the lava of the Deadlands or the depths of the seas...unless he needed the pieces in Tamriel,so the proximity could,in theory,make him immortal.I know this is a shaky idea,but it always struck me as to why the Hero was called the Eternal champion while the CoC was simply called the CoC,was it because the CoC had not yet gained immortality?
I don't really have anything for Battlespire.I did have a theory that the Hero mantled Mehrunes Dagon,but that got debunked rather quickly...maybe the hero never returned to Nirn,and he is still after Mehrunes to finish him.Foolish,but plausible.
But why do the heroes disapear?Well,this is possibly the shakiest bit,but,what if all the Heroes were alive at one time and in one place?I'd imagine Tamriel couldn't handle the amounts of immortals,and a dragon break would happen.Or they may dislike eachother,and a fight of epic proportions would take place.I think the Heroes know this,and they either willingly die in battle or through other means,go to Oblivion,or spread themselves out across Nirn?
So...what do ya think?Maybe I should wait to see what happens to the Heroes in Skyrim,but meh.