Arwen's Mortality

[Legolas]

They had to choose for themselves. The choice would simply dictate the action. It was certain that Elrond would leave. His departure date was the tentative "deadline" for his children's choice, though we see that Elladan and Elrohir took a little longer to decide. Appendix A, Lord of the Rings:

To him therefore was granted the same grace as to those of the High Elves that still lingered in Middle-earth: that when weary at last of the mortal lands they could take ship from the Grey Havens and pass into the Uttermost West; and this grace continued after the change of the world. But to the children of Elrond a choice was also appointed: to pass with him from the circles of the world; or if they remained, to become mortal and die in Middle-earth.

I think it was quite well planned. It has a greater purpose within the story. Letter No. 153:

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.