Arwen and Paracelsus

Paracelsus was a Swiss philosopher who believed in elemental beings who do not have souls - but they can get souls by marrying humans, thereby potentially getting into heaven.

I believe that Tolkien's elves work the same way. I believe that Arwen dies because her marriage to Aragorn got her a human soul, and human souls come with mortality in Tolkien's world.

I am less familiar with other mixed marriages in Tolkien's work, but if I remember correctly they all die too.