Being 'half elven' genetically does not mean a being has a choice between mortality and immortality. *Only* Earendil's family was given the choice, and it would not extend forever - the choice would stop with Elrond's offspring. The family was only given this privelege by way of Earendil's great deeds and the impression it left on the Valar.
Additionally, aside from a strange pairing that led to the line of the Princes of Dol Amroth, elves and men did not reproduce - literally a three-time event (Beren-Luthien/Tuor-Idril/Imrazor-Mithrellas). It was far from 'often' or 'occasional' - not even frequent enough to be described as 'rare.' Three times in history...that's all.
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like Luthien, or is it that one of thier parentswas human and one was an elf, like Earendil? But then again, Earendil had the choice too.
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Luthien only had the choice after she and Beren both died...Luthien was not half mortal. She was simply given the choice because of her great deeds - it was a favour to her from Eru. This is entirely separate of the half-elven choice.
[I think some of this misunderstanding stems from the movies and their portrayal of Arwen - she is made out to be an elf who is trying to decide if she wants to give up being immortal to be with a mortal...this leads to the misconception that elves have the ability to become mortal if they wish. Not even the Valar have the power to change this...Eru himself has the sole power.]