Valinor and death

“In that guarded land the Valar gathered great store of light and all the fairest things that were saved from ruin; and many others yet fairer they made anew, and Valinor became more beautiful even than Middle-earth in the Spring of Arda; and it was blessed, for the Deathless dwelt there, and there naught faded nor withered, neither was there any stain upon flower or leaf in that land, nor any corruption or sickness in anything that lived; for the very stones and waters were hallowed.” – The Silmarillion by J.R.R. Tolkien.

So, how is it that Bilbo, Frodo, Sam, and Gimli die in Valinor if the Deathless lives there?

If nothing faded or withered than how could they die? I mean this says there was no corruption or sickness yet the hobbits and Gimli (doesn’t that sound like a band? “The Hobbits and Gimli”, I mean.) apparently get there and then die?

Yeah, I never got it either.