The only hint we get is in Ceeborn's words to Aragorn when they part:
But Celeborn said: ‘Kinsman, farewell! May your doom be other than mine, and your treasure remain with you to the end!’
For whatever reason, Celeborn is doomed to remain in Middle-earth when Galadriel sails west, even though he quickly "wearies" of his lordship and goes to Rivendell for his remaining years.
As for why Tolkien made that literary choice, it is to set up the ending of the Tale of Aragorn and Arwen.
My point is not that he made that choice but why he wrote it that way. Arwen dies in an empty Lothlorien, wherever Celeborn is.
What fascinates me about the professor is that every main character Bilbo and Frodo's story meets has deceased spouses Elrond, Thranduil, (Dwarven wives are not mentioned) and then Elrond, Treebeard, Theoden, and Denethor.
Unions are only used where there is a specific dynamic Beren, Tuor, Turin, Aragorn and Faramir the latter of which was uncharacteristic and well written in the books.
It exists in the shire but only to reflect the zeitgeist of cosy domesticity in the English Countryside.
For me, the most undeveloped union is Thingol and Melian and the character of the former which suffered from the shifting and evolution of the story. One of the most nuanced characters was the mother figure of Turin. If the story of Hurin had been fully developed as he envisioned it; as the central story of the late First Age, I suspect she would have become more and more important in driving the narrative's emotion.
One could argue this has nothing to do with the ROP. And yet the writers are aware of it in the form of Durin and Disa which is a very worthwhile extrapolation and use of the dynamic.