When the Nazgûl lose their bodily form, what happens to their rings?

[Inziladun]

Originally Posted by Morthoron

I don't think Tolkien reconciled the nine rings conclusively. It's one of those plot holes pitting the fabric of such a sprawling tale. And the inconsistency in the plot logic is nowhere more noticeable than after Isildur cuts the One Ring off Sauron's finger. If Sauron had the Nine, then they would have been lost in the fall of Barad-Dur (which would not be raised again for centuries).

If we accept that Sauron had the One with him in Númenor and was somehow able to trasport it with his disembodied spirit back to ME, why could he not have done the same with the Nine after his defeat by the Last Alliance?