[I'm quite surprised to find minimal discussions on this topic, so forgive me for possible repetitions.]

To avoid any confusion on basis of definition, I would like to say by immortality, I purely mean immunity to the aging process. Not immunity to death, not connections to Atherius, and certainly not becoming a daedra of any sort. All I assume restoration is capable of is the simple prospect of enduring youth, and I will list a few reasons to defend that assumption.

First and foremost, many mages over the ages have been able to achieve immortality with magical forces in one way or another, citation is not included, but unnecessary. Under the assumption that they used one of the basic schools to achieve this, not including un-death, we can derive a simplistic posses of elimination:

conjuration (Summoning can prolong your life? Not out side combat. )

mysticism (My knowledge of this school in particular is limited, but I see so spell in this school that could prolong life.

illusion (Casting illusions will certainly not cure age)

destruction (Absolutely not this one)

alteration (Perhaps, but only where it merges with restoration.)

restoration ( The only remaining school is restoration.)

In addition to the above approach, anyone who views age as any type of illness would have to concede that restoration magic could cure age as it can cure any known sickness.

Also, we learn during dawnguard,(or perhaps earlier) that vampires achieve immortality by consuming, "life blood" from their unfortunate victims. Put bluntly, restoration is defined as, "the masterly of life forces" coincidence? Perhaps, but perhaps mastering these life forces may prevent age.

Finally, in response to a common counter-argument of why this method of, "easy" immortality has not been widely used or even accepted as truth by most masses is that restoration is the most recent school to form. [http://www.uesp.net/wiki/Lore:Restoration] You might wonder why it took so long to create a spell to cure any illness. Perhaps this elusive question might apply to aging?

Interesting idea. Assuming that death of old age comes about in the same manner as in real life then the denizens of TES would simply need to be able to cure disease, repair damaged tissue and rejuvenate aging cells. If a mage could heal accurately on a cellular level then keeping oneself Biologically Immortal would be fairly easy. However, could a mage heal on a cellular level?

Restoration has to be the reason mages can prolong their life, but there must be some flaw or limitation as death inevitably comes (excluding Fyr).

I think the simple answer to the question is actually that it takes an incredibly talented talented mage to actually prolong his life indefinitely with magic, regardless of the school in question. I would imagine that using Restoration to prolong your life for an extended amount of time would be far more difficult than using a method like: Vampirism, Lichdom, extending one's life through necromancy or rarer methods like the one Umaril used.

I've always thought of Alteration as being capable of extending one's life. You mention that you do not think this is possible without combining it with restoration but I think a powerful enough mage would be able to use alteration alone to extend his life.

I could see Mysticism and/or Conjuration being used to do the old soul/mind transfer. Transfer everything that makes up "you" into another body or even an item.

I also like to think that Alchemy (while not really magic) holds the potential to prolong a person's lifespan. These potions would be incredibly rare and the ingredients themselves would be notoriously dangerous and difficult to find. They are sold to royalty and the richest of men for fortunes. And who knows? Maybe these potions only grant you an extra ten years? Twenty? A thousand?

Just like in any aspect of magic there are an infinite amount of spells, each working differently and having a different effect. You wouldn't be able to know whether or not your spell has actually worked or not... ever. A mage could cast the spell he spent a decade working on in the hopes of extending his life. He finishes it... did it work? He has no way of knowing. In ten years he may realize, as he stares at his balding head, that it did not.

And even if it did work the question is: to what extent did it work? Is the mage aging at half the speed? A quarter? A tenth? Will he even be able to recognize that he has aged at all (even a hundred years after his spell) if he is aging at such a slow rate? The aging process would be so slow that it would be unnoticeable. Did he ever not have that sore back? He certainly remembers having it thirty years ago but was it there fifty years ago? Maybe it was... maybe it wasn't.

There is also many ways someone could go about extending their life. They could slow the aging process down like the example above. But they could also attempt a spell that reverses the aging process. They cast the spell and they appear ten years younger. Obviously for this example you can tell that the spell worked although that may depend on whether the spell is instantaneous or gradual.

Perhaps the spell that slows your aging needs to be re-cast every year, every month or every hour. Maybe the spell does in fact cease the aging process entirely but needs to be re-cast every hundred years. The poor mage would think he had prevented his aging indefinitely only to have it resume a hundred years later but he wouldn't notice that he had begun aging again until a significant toll had been taken.

The effects of such an advanced spell is undoubtedly near-impossible to accurately predict, leading to any of the issues above and many more that have already come to mind.

Also to note (and you probably already know this) is that the schools are a mortal creation... that is to say that if someone wanted to they could split magic into a hundred different "schools". Many spells probably blend two or more schools together (obviously this cannot be represented in-game). Also to note is that the traditional six or seven schools don't encompass magic in its entirety. What I mean by this is that there are no doubt spells that do not conform to the rules and that defy categorization. I would expect that many methods of immortality would lie in these... more "uncharted" areas of magic.