Os Nazgûl mantiveram seus Anéis de Poder?

Não, Sauron segurava os Anéis dos Nazguls.

É mencionado em alguns lugares:

Carta 246:

... Sauron, who still through their nine rings (which he held) had primary control. ...

Sociedade do Anel, quando Gandalf diz a Frodo,

"the Nine [Sauron] has gathered to himself; the Seven also, or else they are destroyed."

Contos Inacabados:

Sauron’s “mightiest servants, the Ring-wraiths, who had no will but his own, being each utterly subservient to the ring that had enslaved him, which Sauron held.”

...

the Ringwraiths “were entirely enslaved to their Nine Rings, which [Sauron] now himself held”.

Sim, eles os usam, de A sociedade do Anel Gandalf diz ao conselho de Elrond:

The Nine [rings] the Nazgûl keep.

Existem algumas passagens que indicam que Sauron "possui" os Nove, no entanto, algumas delas são de antes que se saiba que os Nove deixaram Mordor, e na maioria das vezes apenas indicam que Sauron controla os anéis, não que ele realmente os mantenha.

Tolkien foi bem claro sobre isso em uma de suas cartas:

Sauron sent at once the Ringwraiths. They were naturally fully instructed, and in no way deceived as to the real lordship of the Ring...But the situation was now different to that under Weathertop, where Frodo acted merely in fear and wished only to use (in vain) the Ring's subsidiary power of conferring invisibility. He had grown since then. Would they have been immune from its power if he claimed it as an instrument of command and domination? Not wholly. I do not think they could have attacked him with violence, nor laid hold upon him or taken him captive; they would have obeyed or feigned to obey any minor command of his that did not interfere with their errand - laid upon them by Sauron, who still through their nine rings (which he held) had primary control of their wills...

Das Cartas de JRR Tolkien #246

Então aí está. Sauron manteve e segurou os nove anéis e os Nazggl não os usaram.