[Mithadan]

At the close of the First Age, the assorted half-Elves, Elrond, Elros, Earendil and Elwing, were given the right to choose between being counted among the First Born or Men. Only Elros chose to be mortal, though it seems that Earendil might have so chosen but elected to be counted among Elvenkind due to Elwing's wishes.

Elros' decision bound him and his offspring. I have always believed that the decisions of Elrond, Earendil and Elwing were also binding upon their offspring and that Arwen, by choosing to remain in Middle Earth, did not change her fate. She died out of grief, but entered Mandos and could eventually emerge just like any other Elf that perished. Others believe that the children of Elrond could also choose to be mortal. This would be inconsistent, in comparison to the fate of Elros and his line, so personally I don't follow this interpretation.

Another possible line of reasoning is that Arwen, by giving up her right to return into the West and gifting this right to Frodo, became mortal. However, Tolkien has stated in Letters that Frodo, Sam and (if he indeed did follow Legolas) Gimli all died in the West, so the idea of Arwen gifting her immortality to Frodo is flawed.

As for the royal line in Dol Amroth, they were longer lived than other Men though this may be more because their Numenorean blood was "purer" than due to the (legendary) marriage with Mithrellas. The choice of the Half-Elven was given only to those living at the close of the First Age, not to later unions between Men and Elves.

I use the term "legendary" in connection with Mithrellas, because it is repeatedly mentioned that there were only three unions between Men and Elves, Beren and Luthien, Tuor and Idril and Aragorn and Arwen. All were considered extraordinary events. So the Mithrellas legend may be just that, a story.