Elrond (who was 50% Elven) lived well over 6,000 years before departing Middle-earth.
Because of his distant Elven lineage Aragorn lived over 200 years before he died. As a 3/4 Elf Arwen was immortal and lived for 2901 years before dying of grief (after the death of Aragon).
Their son Eldarion would have been at least 37.5% elven. Should he expect his lifespan to be somewhere between Arwen's and Aragorn's? Or does he have enough Elven blood to live forever?
In a late writing c.1959, Tolkien works out the aging of various Elvish or mixed Elvish characters.
Eldarion was mortal and was not by promise included in the "grace of Eärendil", but he had in fact a long youth: which took the form of remaining like a young man from maturity at 20 until 60 without change. He then lived another 65 years: making him 125, but in life-age 20 + 65 = 85. His descendants became normal, but long-lived (80-90).
The Nature of Middle-earth - "Ageing of Elves"
As you may know, Elrond and his brother, Elros, were half-elven, the sons of Eärendil and Elwing. The Valar gave them (along with the other living half-elves) the choice to follow either the path of the Elves or the path of Man. Elrond chose his elven side, remaining immortal, and Elros chose the Gift of Men and becoming the first King of Númenor. His line did not have a choice and were all thereafter mortal men, though with a very long life span (and some of his descendants, especially in later years, begrudged him that choice). Elrond's children were immortal until Elrond sailed west to Valinor, at which point they were given the choice to follow him there or remain in Middle-earth and become mortal. Arwen chose to remain to marry Aragorn. Thereafter, both being mortal, their child, Eldarion, was also counted among men. From the LotR wiki:
[Arwen] exercised this option [remain and become mortal], marrying Aragorn II Elessar, king of the Reunited Kingdom, and finally dying at the age of 2,901 years. Their son Eldarion and their daughters were not counted as Half-elven, but rather as Dúnedain restored.
So we know he's mortal, but not precisely how long he'll survive. I would wager, because of the renewed elven blood in his veins, around the same 500 years Elros's line started out at.
The differing longevity of the descendants of Eärendil have nothing to do with the percentage of Elven blood. Rather, it's to do with which kindreds they chose to be counted amongst.
Elros and Elrond made their choices at the end of the First Age. Elrond's children, in turn, were also allowed to make the choice, but this did not have to happen until Elrond sailed over Sea.
When this eventually happened, after the end of the War of the Ring, Arwen made the irrevocable choice to be counted among Men. Thus, although by inheritance Eldarion might well be thought of as "half-elven", from the point of view of kindred he was fully a Man, and therefore not immortal. We don't know how long he lived, though.
The only explicit statement is in Letter 338:
I have written nothing beyond the first few years of the Fourth Age. (Except the beginning of a tale supposed to refer to the end of the reign of Eldarion about 100 years after the death of Aragorn...)
Aragorn died in Fourth Age 120, so the reign of Eldarion was therefore from Fourth Age 120 to 220 (or slightly later).
There's no record that I can find of his birth in the Tolkien sources I've checked (The Lord of the Rings and History of Middle-earth 12) but some on-line sources (e.g LotR fandom wiki) record an uncited date of Fourth Age 43. I can't personally vouch for the reliability of this source.
In any event Eldarion can't have been born much before Fourth Age 1.
This gives an age range for him of from 177 to 220 (or slightly more). Since Aragorn lived to 210 (and since the LotR wiki has proven to be an unreliable source in the past), I'd personally incline towards the high end of this range.
Elves and Men have different fates. The souls of Elves are bound to Arda so that even if their bodies are destroyed they can come back in another body. Men are not bound to the earth which is why they are known to the Elves as "the visitors".
Elrond is called half-Elven but he is 100% elf, just as his brother Elros was also half-Elven but 100% Man. In Note 1 to The Line of Elros there's this part:
Elros was granted a peculiar longevity (he lived to 500 years), and it is said here that he and his brother Elrond were not differently endowed in the physical potential of life, but that since Elros elected to remain among the kindred of Men he retained the chief characteristic of Men as opposed to the Quendi: the "seeking else-wither," as the Eldar called it. the "weariness" or desire to depart from the world.
When Arwen made her choice, chose her fate, she became part of the kindred of Men. There is no way her fate will mimic that of an Elf, because she is mankind now. I would assume that her son would probably live like most of Aragorn's forebears did, between 155-160 years of age. The life-span of the Dúnedain continued to wither in Middle-earth.
Until Aragorn it had been about 1000 years since any Dúnedan lived to at least 200 years. The last to do so in Gondor as recorded in the Annals was king Calimehtar, and in Arnor the last was Malvegil which was about 1700 years prior to the War of the Ring.
In all honesty around maybe 170 - 250 years he could have lived. By Aragorn's time even most pure of Gondorians and Arnorians (Dúnedain) lived around 100 - 110 years, greatly diminished from their time in Númenor (420 - 250 years). The only man to surpass 420 years was Elros Minyatur, First King of Númenor and no other. He lived to the super-old age of 500. After him the lifespan goes in decline (from the 11th King onwards the expectancy is 250 - 350 and by the 26th King they live around 210 years).
Even the House of Dol Amroth (descendants from Númenor and Sindar blood) by the Late Third Age lived around 110 years and most commoners live pretty normal (like ours) lives (75 - 90 years). Only Aragorn and his line seem to surpass that with 210 years, the same as the Kings of Númenor before the fall.
So we can assume that Eldarion lived around 170 to 210 years old, that is if the decline does not continue after Aragorn. He could have lived less and his descendants less and less until they became us, regular normal humans from our history.
I would expect Eldarion to live close to 500 years like the kings of old. As Arwen had a choice to be elvish or mortal, the line of her decendants should be about the same as Elros' first decendants (possibly a bit shorter as Aragorn only lived to be about 210)
Eldarion would have live at least for 200 years as he was the son Aragorn who also lived for almost 210 years. Eldarion's life expectancy may vary around 200. It would definitely not have been 500 years as that of Elros because Arwen became a mortal woman when she bore King Elessar his son and was no longer an Elf.
In Tolkien's sagas, life-spans of "Half-Elven" progeny do not "decrease" from that of the mortal parent - they increase significantly. This is due quite obviously to the 50% influx of the true-immortal blood of the Elven parent. Eldarion would thus not live "less long" than his mostly mortal father - as his mother Arwen was a true immortal-High-Elf of Noble lineage.
Indeed, Arwen's lineage actually has more immortal Elvish blood than her father Elrond and uncle Elros. She is also only one generation more removed from her great grandfather Dior - who was 1/4 Maiar-god. Elros and Elrond are 3/8th human (by their human Grandfather Tuor; and 1/2 human Grandfather Dior). Arwen is only "3/16ths" Edain - so in theory and in mathematical fact: her true-immortal DNA is far stronger and more pure.
Aragorn also is not a mere "Dúnedain", but in fact he has some "Elvish Blood" as a direct descendant of Elendil and Elros. The Lords of Andúnië were all descendants of Silmariën - the firstborn-and-daughter of the 4th King-descendant of Elros (and arguably, the true-heir to the throne). So too does Aragorn have "a trace" of immortal Maiar-blood. This does not include any additional later influx of the "Blood of Elros" by Andúnië-marriages to more female descendants of Elros. There should/would have likely been several due to the close relationship and alliance between the Kings of Númenor and the Lords of Andúnië. (It can be speculated that in later generations, the Lords of Andúnië actually had more Blood of Elros in their line than the later Kings did, due to the majority of children not becoming "king" - and marrying then into the line of the Andúnië.)
We do have several, several examples of the "lifespan" of Half-Elven children like Eldarion (notwithstanding "choices" about ending one's life early and "choosing to die", as apparently most royal half-elves "choosing" a mortal life do). Dior, Eärendil, Lúthien, Elwing, Eluréd, Elurín, Elladan, Elrohir and Arwen were all "half-elves" - and were all, essentially, Immortal - living in many cases thousands of years. Arwen later "chose a mortal life" and willed herself to die (of grief) at the age of 2,901. Elros too "chose to die" on his 500th Birthday.
Elros, like Arwen, had sons with mortal humans - although as mentioned: Arwen's blood was more-pure with immortal non-human lineage. Also, Arwen's mate Aragorn had trace Evlish blood as well - unlike the merely-human wife of Elros. Eldarion, thus, should live at Least as long as Elros's son Vardamir - who "decided" to die at 471 years old. Any other grandsons or great grandsons of Elros that are recorded all lived past the age of 400. The likely-greater life spans of all other descendants are not recorded, including those not burdened by the stresses of leadership, and all females with universally greater average lifespans than males.
The potential lifespan of Eldarion should be at least that of the less-immortal-blooded Vardamir: 471 years (or longer).
We have no real precedent for predicted lifespan for this situation. Dior, the son of Beren Erchamion and Lúthien, died an early death in Menegroth. Eärendil the Mariner, son of Tuor of the House of Hador and Idril of Gondolin, was granted immortality to sail the Heavens with the last Silmaril on his brow. Eldarion is the only child of Man and Elf to live out his days.
Eldarion and his siblings embodies the long sundered branches of the half-elven, as Aragorn and Arwen are both descendants of the ancient bloodline of the earliest unions between men and the eldar (Beren-Lúthien, Tuor-Idril), thru Lúthien, both Aragorn and Arwen inherited Maiarin blood thru Melian of the race of the Ainur. Eldarion, being an odd mixture of all these races, is expected to have a very long life perhaps to match that of Elros Tar-Minyatur of Númenor. But for me, if Arwen delayed her choice of race, perhaps her children will be accounted as part of the half-elven, but dying mortal means her children will have to accept the Doom of Men though they have been given indefinite life-spans as children with the blood of the mightiest of the eldar and of the high race of the god-like Maiar both of the immortal beings of Arda.
