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This sounds a lot like The Farthest Shore by Ursula LeGuin, book 3 of the Earthsea Cycle.
Over 20 years old, check (1972)
Third book in a trilogy, check (books 4 and 5 were added much later than the original 3 books in 1990 and 2001.)
World of islands referred to as the Archipelego, check. (Also called Earthsea.)
"Something" consuming/sucking the life out of the islands/people from the edges and working toward the center, check.
Prince from the center island, check.
Female lead from island at the edge of the archipelego, well, that's book 2, The Tombs of Atuan, and book 4, Tehanu.
I don't remember that prophecy at all.
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