I guess because they were tied to the 9, which in turn was tied to
the One?
This seems to be the concensus from the reading I've (quickly) done.
Because
Sauron directly enslaved them by the gift of the controlled rings, their fate is said to be tied to Sauron's power - "rather to
the One Ring's" directly.
"They could only be harmed by
weapons having spells on them."
The
Witch King of course also had a prophecy in view, which was 'he would not be killed by a man.' Which is true.
The blade made in the
North-kingdom used by
Merry "had spells" tied to it, which undid him... then the blade driven by a woman finished his
current form off. It is uncertain, given that their fate is tied to the One Ring.
(Remember when they were unseated from the
horses at the ford and 'lost their black cloaks which gave them form' on their attempted passage across into
Elrond's land, they were disembodied and were "crippled without their hoirses" - and their cloaks gave them their shape and form. They needed to reform again. As
Gandalf said, "...there is nothing more to fear from them
at present.")
Given that the One Ring still existed, who knows. Had it not been destroyed soon thereafter, it is possible the Witch King could have reformed yet again, or maybe even was by the time they came to the Gate to distract the unsuspecting Sauron.
"At his summons, wheeling with a rending cry, in a last desperate
race there flew, faster than the winds,
the Nazgûl, the Ringwraiths, and with a storm of wings they hurtled southwards to Mount Doom."
Tolkien, J.R.R..
The Lord Of The Rings (p. 946). HarperCollins. Kindle Edition.
While Tolkien does not specifically say 'the 9..." neither does he exclude the possibility.
"Man has probably (an
Elf would say) a higher if unrevealed destiny than a longeval one. To attempt by device or ‘magic’ to recover longevity is thus a supreme folly and wickedness of ‘mortals’. Longevity or counterfeit ‘immortality’ (true immortality is beyond Eä) is the chief bait of Sauron – it leads the small to a
Gollum, and the great to a
Ringwraith."
.... Tolkien, J.R.R..
The Letters Of J.r.r. Tolkien (p. 286). HarperCollins. Kindle Edition.