As Voronwë noted, suffering in a land can help form attachments:
"Yet not all the Eldalie were willing to forsake the Hither Lands where they had long suffered and long dwelt; and some lingered many an age..." JRRT, conclusion to
Quenta Silmarillion, The Lost Road And Other Writings
They were connected but always in the concept of their immortality. For as long as they could retain their environment unchanged.
I think it's a bit more complicated. In Tolkien's world we have plenty of Elves who refused the original summons to the West (
Avari "Refusers"), and Elves who had been in the West, fared to Middle-earth, and were allowed to return again (the Exiled Noldor, except for Galadriel) and yet remained without promise of any rings of power.
Middle earth wasn't their "place" as all other species, men, dwarves, animals and the environment that they lived in, had limited lifespan. That becomes very clear in all of the books. All elves have some kind of sorrow, Tolkien describes all of his elf characters as fair, ageless, untouched by time and in a state of sorrow.
Generally speaking, it's true that the relatively quick ageing of the world around them becomes a grief to the Elves, but what might this then say about their love of home? Galadriel says (although granted,
she is using Nenya to stave off the unwanted effects of time), given the possibility of the destruction of the One:
"The love of the Elves for their land and their works is deeper than the deeps of the Sea, and their regret is undying and cannot ever wholly be assuaged. Yet they will cast all away rather than submit to Sauron: for they know him now."
The sea-longing existed during the Second Age too, but the elves didn't leave either. They used their rings of power to retain their strongholds and places, and remained isolated in their own communities. The Noldors didn't have the right to go back, but what about the Sindars and the Silvans that were actually of Teleri origin?
The Exiled Noldor, except for Galadriel, did have the right to return in the Second Age, but it's some one thousand five hundred and ninety years before the Mirdain complete the Three, and only ten years later that Celebrimbor perceives the designs of Sauron (and so, I assume the Three are taken off). The Three were in use in the Third Age
"while Sauron slept" (Appendix B)... the question of Círdan aside here.
Tolkien notes of the Sea-longing and the Noldor:
"But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss." JRRT, The Road Goes Ever On
Let me give you another example of how some stories have.... continuity errors! It is something that I noticed the other day while I was reading the Chronology part at the end of the Lord of the Rings.
Before I move on to the Arwen matter, I don't consider any continuity errors to be true "errors" unless a seemingly clashing description/detail/what-have-you has been author-published.
Or... canon!
(that last bit's for you Voronwë
)
So Arwen was 2690 year older than Aragorn, something that makes her... quite an old maid even for elven standards according to what Tolkien wrote in his Laws and Customs of the Eldar about the Elves that supposedly got married at a rather young for their standards age. So how did it happen and Arwen was unmarried (such beautiful and high born lady!) for 2710 years, until she met Aragorn during his twenties?
Technically Arwen was not an Elf but one of the Half-elven, but that aside,
Laws and Customs of the Eldar was not published by JRRT himself. And for example, I think there's late evidence that Tolkien abandoned his idea in L&C concerning the Elven maturation rate in Middle-earth.
Or, Christopher Tolkien at least seems to think his father might have abandoned the concept (also in L&C) concerning the Noldorin Chosen-names, for instance. And in L&C, Tolkien had yet to revise his thoughts about Elvish reincarnation...
... in short, L&C's an interesting text; I use it (see below), but in my opinion Tolkien need not feel bound to any one idea in it, the next day, nor ten years later (if he even remembers "X" ten years later, that is).
Also, if you don't fall in love until you are around nineteen or twenty Elvish-Long-Years old, you might not marry no matter what the custom is. I'm not sure I would call that a continuity error even considering the relevant description in L&C as a "must be", so to speak.
The romantic element of her abandoning her immortality for Aragorn's love doesn't have the same impact if you realise that she had already lived for 2710 years. When he died after another 150 years she was already 2860 y.o. Not in her first youth, even for elven standards!
One could see it that way, I admit, but I think one could look at the same circumstances and argue that it has a nice impact, arguing that Arwen had had a taste of "immortality", and had seen/at least been aware of, the swift death of mortals, and still abandoned an Elvish fate for Aragorn. Or, an Elf might see Arwen's choice as a way to escape "immortality"!
In Middle-earth, the Elven "limited immortality" can itself become a burden, but yet -- if I may now refer to a section of the... ah... "questionable text" L&C (LOL!) -- we even have some Elves who will live long enough in Middle-earth so that their bodies actually fade to memory.
Ahem... cough. If that last bit's truly true for you
This is my first post and first thread on this discussion board. My name is Gilgaearel Baen and I warn you that English is not my first language as I'm an Elf after all. 
