[Mithalwen]

Celeborn's history went through several versions so there may not be a definitve answer. Certainly I can't recall anything in any of them (though my readling of HoME has not been consistently thorough) that gives any reason that Celeborn should be forbidden to pass in to the West.

Hammond and Scull in the LOTR reader's companion refer to the abandoned Epilogue in which Sam tells his daughter that Celeborn still lives in Lorien and has not tired of his own land - when he does he can leave and points out that it is only a very short time in Elvish terms.

They say that this refers to an early version of Celeborn's history and refer back to abn extremely lengthy note on "The Mirror of Galadriel" which commences with a quote from Christopher Tolkien "There is no part of the history of Middle-earth more full of problems than the story of Galadriel and Celeborn" [and who are we to argue? !].

The comment on Greenie' quote then refers to Appendix B and the Prologue which state that Celeborn soon went to join his grandsons at Rivendell but there is no record of the date he sought the havens. It also refers to an unpublished letter to a reader which says that as Celeborn had never lived in Valinor and would remain until he saw the beginning of the dominion of men but the separation would be brief in Elvish terms.

I suspect that his remaining may be linked to the postponed choice of Elladan and Elrohir for whatever reason that was. It is a plausible that he might remain either for his grandsons to be ready to leave or if they chose not too, horrific though the experience no doubt would be) until their mortal lives ended. However since
I get the impression that Arwen died alone in Lorien, my guess would be that at some point in between the passing of the Ringbearers and the death or Arwen, Celeborn and the twins left.