Elrond's children (or any
elf, really) can choose a mortal life but Man (even the Numenorians) cannot elevate themselves to immortality with the
Elves.
There is one coincident of an Elf achieving a mortal fate, which is
Lúthien who asked to change her fate so she could be with
Beren. It says that
Mandos was moved by her plight and restored them both to life, but as it is made quite clear that it was
Eru who granted immortality to the Firstborn and offered the Gift to
men, and that the
Valar could not change that, Luthíen’s request was granted due to Eru’s intervention (and likely only because Beren and Luthíen still had a part to play in the music of
Arda).
And then there is
Tuor, who was (possible) granted the life of the Eldar. Perhaps it was because of Luthíen being allowed to follow Beren where no Elf can go that Tuor was gifted with the fate of the Eldar - to restore the balance…
Then there are the half-elves, and I agree with what Nóm said. The way I see it, the choice of the
Peredhil essentially comes down to choosing their fate. Only two fates exist: Elves (Valar and
Maiar) exist as long as Arda exists and they “age” as Arda
ages. Mortals die and pass beyond the circles of Arda, and they age at a much quicker rate.
So when
Elros (and
Arwen) chose the fate of Men their biological clock was set to “mortal” time (not so much in the sense of aging at the same speed as mortals, but more in the sense that their time in Arda was limited. Elros’ elven blood, for instance, gave him a longer lifespan than all other Men). And this seems to me to be the reason why Elros’ (and Arwen’s) descendants had no choice when Elrond’s children did. Elros chose mortality so his biological clock was not tuned to Arda, but to that of mortals, and his children, being born of that blood, moved in sync with it. To go from mortal to immortal life would be immeasurably hard.
It seems far “easier” speed up the aging process, which (in the case of Elrond’s children for as long as their father stayed in
Middle-earth) has been in sync with Arda, rather than the other way around.
Also, the “small” matter of fate plays a major role:
Immortality and Mortality being the special gifts of
God to the Eruhini (in whose conception and creation the Valar had no part at all) it must be assumed that no alteration of their fundamental kind could be effected by the Valar even in one case: the cases of Lúthien (and Túor) and the position of their descendants was a direct act of God. The entering into Men of the Elven-strain is indeed represented as part of a Divine Plan for the ennoblement of the Human
Race, from the beginning destined to replace the Elves.
The view is that the
Half-elven have a power of (irrevocable) choice, which may be delayed but not permanently, which kin's fate they will share.
(Letter No. 153)
It is interesting that even Arwen, one who had somewhat lived as an elf up until her decision to become mortal, was prone to that fear of death that afflicts man as a result of his original Fall. One would think that being of elven culture and wisdom, that she of all women in Middle-earth would be at peace to accept the gift given to Men, especially since it would mean that her and
Aragorn (who accepted his fate) might stay together beyond the confines of the world.
I think the reason Arwen feared death was because she, like Eärendíl, chose to be with her beloved rather than choose the kindred her heart belonged too. Also it says that she “was not yet weary of her days…” (Appendix A), so being Elven of nature, and not tired of the world, was what made mortality especially bitter for Arwen. I believe that had Arwen been weary of the world at the time Aragorn laid down his life, they would have gone together like Beren and Lúthien.