There is now no ship...

[zxcvbn]

Two things:
1.Arwen was now a mortal woman. Mortals are not permitted to travel to the Undying Lands, with very few exceptions.

2.She had already given up her place on the ship to Frodo.

[Sauron the White]

Yes, Arwen gave up her spot on the ship to Frodo. But many years later Legolas built a new ship that could have accomodated her. And since exceptions were made - for even a dwarf - could not one be made for the daughter of Elrond?

The ideas that ring most true with me are the ones that she simply did not want to leave Aragorn behind even in death.

[CSteefel]

I am not sure that it was clear that Gimli was going to the Undying Lands. Or if he was, then it may have been more like a Purgatory, as it was for Frodo. Even Frodo did not apparently stay there, since it is not in the power of the Valar to convey immortality on any mortal.

As for Arwen, I am not sure that she did want to remain, at least once Aragorn died. In Appendix A, as Aragorn prepares to die, it is clear that she now fully realizes the bittnerness of her mortality

...and thus she tasted the bitterness of mortality that she had taken upon her.

and she says

...there is now no ship that would bear me hence, and I must indeed abide the Doom of Men, whether I will or I nill: the loss and the silence. But I say to you, King of the Numenoreans, not till now have I understood the tale of your people and their fall. As wicked fools I scorned them, but I pity them at at last. For if this is indeed, as the Eldar say, the gift of the One to Men, it is bitter to receive.

And beyond this, she did not seem to cling willingly to her mortality, and in fact

...Arwen went forth from the House, and the light of her eyes was quenched, and it seemed to her people that she had become cold and grey as nightfall in winter that comes without a star.

I don't read this as a case of Arwen willing so much to remain behind (at least once Aragorn died) as now realizing the full bitterness of her situation...

[TheGreatElvenWarrior]

I do think that Arwen needed to die, not because I didn't like her, but because Arwen would find no healing in Valinor or happiness, once Aragorn died she had no desire to live... At least when Frodo went he still had Bilbo and maybe later Sam, and he was going to die so that means he would not need to cry, yes it is sad when someone you love dies or is seen no more(I have cried many times over my cat that has died and my other cat that was sent away) but I would think that once your true love dies it is different.

[Lord Gothmog]

When Elrond left Middle-earth for the West, the time came for his childern to make their decisions as to which people they would have their fate joined to, Eldar or Men. The brothers Elladan and Elrohir seems to have been able to 'delay their decision' by staying for a time in Imladris with Celeborn. However, Arwen did not delay, she made her decision to join her fate with that of Men and marry Aragorn.

There are some choices that do not allow for one to recant or change. This was one of them, in making her choice to join with Man she closed the door to the West. The same decision (with the same result) was made by Elros and he was in a better position to recant his choise and travel to The Undying Lands He was almost in sight of them. This is why There is now no ship that would bear Arwen into the West. She was no longer allowed to go.

As for Gimli, we are not certain that he did go into the West as this is only what the Hobbits heard after Legolas left. However, even if he did do so, we do not know the reason why he would be allowed even as far as 'The Lonely Isle'. The only ones we know of for certain are Bilbo and Frodo, both of whom were allowed into the West to have a chance to heal in sprit before dying and leaving Arda.

[Lindale]

Originally Posted by Lord Gothmog

The same decision (with the same result) was made by Elros and he was in a better position to recant his choise and travel to The Undying Lands He was almost in sight of them. .

Where was this stated Lord Gothmog? In one of the latter HoMEs, or the Letters?

Arwen chose to be mortal, and even if she did go to the West she's already mortal. And she'll die. The mortals who went to Aman, they don't lose their mortality. But they get healed, pretty way better than in ME anyway. But for a lovesick elf-turned-mortal much like Luthien was, I think no amount of beauty or bliss can heal that.

[Lord Gothmog]

It is stated in the published Silmarillion and in Letters.

From the Silmarillion: Chapter 24: Of the Voyage of Eärendil and the War of Wrath

It is told among the Elves that after Eärendil had departed, seeking Elwing his wife, Mandos spoke concerning his fate; and he said: 'Shall mortal man step living upon the undying lands, and yet live?' But Ulmo said: 'For this he was born into the world. And say unto me; whether is he Eärendil Tuor's son of the line of Hador, or the son of Idril, Turgon's daughter, of the Elven-house of Finwë?' And Mandos answered: 'Equally the Noldor, who went wilfully into exile, may not return hither.'
But when all was spoken, Manwë gave judgement, and he said: 'In this matter the power of doom is given to me. The peril that he ventured for love of the Two Kindreds shall not fall upon Eärendil, nor shall it fall upon Elwing his wife who entered into peril for love of him; but they shall not walk again ever among Elves or Men in the Outer Lands. And this is my decree concerning them: to Eärendil and to Elwing, and to their sons, shall be given leave each to choose freely to which kindred their fates shall be joined, and under which kindred they shall be judged.'

This shows that Mortal Man was not allowed to go to the Undying Lands. When Elros and Elrond made their choices Elros became numbered among Men and therefore was no longer permitted entry to Aman or even The Lonely Isle. Arwen made the same decision to be numbered among Men and therefore could not go to Aman, she would have been refused entry and this she knew.

From Tolkien's Letters:
297 Drafts for a letter to 'Mr Rang'

(The attempt of Eärendil to cross Ëar was against the Ban of the Valar prohibiting all Men to attempt to set foot on Aman, and against the later special ban prohibiting the Exiled Elves, followers of the rebellious Fëanor, from return:

325 From a letter to Roger Lancelyn Green 17 July 1971

The Elves who took this road and those few 'mortals' who by special grace went with them, had abandoned the 'History of the world' and could play no further part in it.

So unless they were given special permission, Mortals were not permitted to set foot on the Undying Lands.