She already made the choice earlier and there is no way to change it. Most choices in life are like that. Truce!
Arwen triumphs in the end. She lost Aragorn, the love of her life, as she knew she would, and then journeys to Lothlorien to the most beautiful spot in Middle-earth and there bids her elvish immortality farewell, consciously dying and fulfilling her choice and pledge. It is sad but beautiful, and she then joins Aragorn beyond the circles of the world.
What she lost was what she had materially gained in the world, and by her commitment, her Elvish immortality. But she gains her will, her choice, her follow-through and very bravely accepts her chosen fate.
Arwen is welcomed as a true hero and blessing to man's lineage when she goes into that Light after mortal death and reunites
:-)