The Witch-King was finally dead, there was no way he could come back. I believe Tolkien didn't simply think mu too much about it when he wrote that "in that age of the world". The other Nazgūl were dead too, they were "alive" only due to the One Ring, and when it was detroyed, so were the Nazgūl. None of them could defy Mandos, and they haven't ever done that. It was Sauron who made them live so long(and kinda defy Mandos), not the Nazgūl.
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"Out of doubt, out of dark to the day's rising I came singing in the sun, sword unsheathing. To hope's end I rode and to heart's breaking: Now for wrath, now for ruin and a red nightfall!"
~Eomer
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