I think the Kokiri, at heart, are walking metaphors for innocence.
This is pretty obvious in some ways, such as them being children their whole lives, but it goes deeper than that. The whole atmosphere of Kokiri Forest is filled with a child-like innocence. They're all just a bunch of kids, playing with (or in some cases, like Mido, bullying) each other all the time. They don't seem to have a care in the world, and they have all the time in the world to play, explore the forest, draw on their houses, talk about how awesome Z-targeting is, etc. The whole place feels like a sweet, innocent neighborhood, filled with kids to play with- not unlike some of our own childhoods.
The reason they have this great innocence? They're surround by the protection of their fairies and their guardian, the Great Deku Tree. I believe the fairies act, in a way, as a metaphor for the children's own conscience. They all have one over their shoulder, and they lead them to the right directions and away from bad ones, much like the angel/ devil depictions in cartoons. For example, take Link's fairy Navi. Although she's pretty annoying, Navi
navigates Link throughout his adventure- "Hey, Listen!" - "Watch out!"- "Look!"
The Great Deku Tree is essentially their parent. He protects them from harm, and it's his job to make sure the Kokiri stay safe and innocent as long as possible. This means that he must protect them from both outside harm (like Ganondorf, by protecting the Forest Emerald with his very life), but also to keep them innocent as long as possible. To achieve the latter, I believe the Great Deku Tree made up the rumor about Kokiri becoming a Stalfos if they left the forest. Not too far-fetched, considering parents tell their children lies to protect their innocence as well, through Santa Claus, the Tooth Fairy, etc.
But to the question at hand- Can the Kokiri die from old age? Or, in keeping with the running metaphor, can our innocence die? Of course. Nothing great lasts forever, including our innocent childhood.
However, I don't think their death would be due to biological reasons. I see it being inevitable that, one day, a Kokiri dismisses their fairies and the Deku Tree's advice and wonders outside the forest. It's only natural- as we grow up and simply live longer, we all start thinking more for ourselves and begin to question our surroundings, and become more curious to see what else exists in the world besides what our parents say there is. Because the Kokiri are innocent children, if they wonder outside the forest, they're inevitably going to be taken advantage of in one way or another, and so they die. And a new Kokiri, I assume, is born in the Forest.
Also, as a side-note, if you continue these metaphors of the Kokiri as innocence and fairies as one's conscience, it really opens up great interpretations of Link & Navi, especially at the end of the game. Man... I love the N64 Zeldas!
And no, I wouldn't say strictly they couldn't die from biological reasons associated with living a long time. However, the way I see it, that probably wouldn't be the typical life-cycle of a Kokiri. They're more-or-less innocent, live in the forest X number of years (still physically children), and they eventually leave the forest. From there, who knows what may happen to them. They could be killed by Stalchildren, starve, run into hostile Gerudos, etc. A typical Kokiri, I'm guessing, would be ill-prepared to face the dangers outside the forest.
