Do we ever get more information about the Entwives?

The TL;DR Version:

No. We don't hear anything else about the Entwives in any of Tolkien's stories. He does write about what may have happened to them in one of his letters, but he doesn't give us anything conclusive. He merely proposes a few possibilities, and tells us which one he considers most likely ("I think Sauron killed them all thousands of years ago"), and which he would prefer to be true ("I hope that at least some of them survived, and will eventually be reunited with the Ents"); as if this weren't noncommittal enough, he ends with "I don't know".

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The Long Version:

Aside from the text of The Lord of the Rings (and the drafts and revisions thereof), all we have is this indecisive tidbit from one of Tolkien's letters. A fan had written to him with many questions, including a question about whether Tom Bombadil had found the Entwives. Tolkien's reply is characteristic Tolkien evasion and refusal to commit; he begins by assuming the worst, more or less saying "They're all dead", but soon softens his stance - albeit only slightly - saying "maybe some of them got away (but might have been enslaved)", then ends on an optimistic but noncommittal note - "I hope they're okay, and I hope the Ents eventually found them, but I don't know":

[Tom Bombadil] has no connexion in my mind with the Entwives. What had happened to them is not resolved in this book. [Bombadil] is in a way the answer to them in the sense that he is almost the opposite, being say, Botany and Zoology (as sciences) and Poetry as opposed to Cattle-breeding and Agriculture and practicality.

I think that in fact the Entwives had disappeared for good, being destroyed with their gardens in the War of the Last Alliance (Second Age 3429-3441) when Sauron pursued a scorched earth policy and burned their land against the advance of the Allies down the Anduin (vol. II p. 79 refers to it). They survived only in the 'agriculture' transmitted to Men (and Hobbits).

Some, of course, may have fled east, or even have become enslaved: tyrants even in such tales must have an economic and agricultural background to their soldiers and metal-workers. If any survived so, they would indeed be far estranged from the Ents, and any rapprochement would be difficult – unless experience of industrialized and militarized agriculture had made them a little more anarchic. I hope so. I don't know.
- The Letters of J.R.R. Tolkien, Letter #144

This is par for the course with Tolkien. Here, as in the stories themselves, there are some hard and fast rules; the most relevant rules, in this case, being as follows:

1. Even his "happy" endings are heavily infused with sadness and tragedy (the point is to maintain hope even in despair).

2. He always insists on maintaining the peculiar point of view from which he wrote the books: yes, he is the narrator, but he is only providing the best information available to him, and he never claims - much less guarantees - that this information is complete, unbiased, or entirely accurate.

Obviously, Tolkien could have written "Sauron burned all the Entwives to death and dug up their gardens"; or he could have written "The Entwives came back home and the Ents were delighted and lots of little Entings were born"; or he could have written "Most of the Entwives were killed by Sauron, but eventually, a few returned, and the survival of the Entish race was ensured"; he could have written anything he wanted to write. But he must have seen more value in uncertainty than he did in any potential resolution to the question of what became of the Entwives.

Thus, we are left with the passage quoted above, in which he tells us that:

• The worst case scenario - the Entwives were wiped out thousands of years ago - is the most likely to be true, but...

• Something slightly less horrible - the Entwives fled, and might have been enslaved - might have happened, in which case it is likely that...

• The Ents and the Entwives could probably never be reconciled, even if some of the latter had managed to survive and eventually went home, but...

• It is still possible that the remaining Entwives came home and were reconciled with their Ent husbands, although ultimately...

• He just doesn't know (but he hopes that the Entwives came back and were reunited with the Ents and made lots of little Entings).

There is a possible exception to Wad Cheber's answer that I've always found intriguing. At the beginning of Fellowship Sam is in conversation with other hobbits at The Green Dragon.

""All right," said Sam laughing with the rest. "But what about these Tree-men, these giants, as you might call them? They do say that one bigger than a tree was seen up away beyond the North Moors not long back."

"Who's they?"

"My cousin Hal for one. He works for Mr. Boffin at Overhill and goes up to Northfarthing for the hunting. He saw one."

"Says he did, perhaps. Your Hal's always saying that he's seen things; and maybe he sees things that ain't there."

" But this one was as big as an elm tree and walking-walking seven yards to a stride, if it was an inch."

Combine that with Treebeard's later comment that he thought The Shire would be the sort of place the Entwives would like and it makes me wonder if this was a thread Tolkien at one point thought to explore and later simply did not.