[PrinceOfTheHalflings]

Sauron was not a slave to his ring, so I don't feel the same sympathy towards him as I do for the other Ringbearers. You should feel more sympathy towards the Nazgul, who were once mighty lords but ended up being utterly subjected to Sauron's will.

I doubt that Sauron immediately knew that the Ring was not destroyed after Isildur took it. For one thing, Sauron was nothing more than a disembodied spirit at that time, and took a very long time to start regaining his powers. Also, Sauron would have assumed that Isildur would have eventually succumbed to the temptation to use the Ring and should have become a Dark Lord himself. Or else, if the Ring betrayed Isildur then surely someone else would have taken the Ring?

Instead, no new Dark Lord emerged. Clearly the Ring was either destroyed or lost, but for a long time it must not have been clear to Sauron exactly what had happened. The emergence of some mighty lord wielding the One was always Sauron's greatest fear, especially at a time when Sauron did not have the strength to oppose such a power and take the Ring back by force. Few could have controlled the Ring, but perhaps there were those with the strength to do so. Galadriel or Elrond, for example. Sauron would have especially feared someone of their stature as Ringbearers.

After a time, and it may have been many years, Sauron would have started to "rebuild" himself and must have realised that the Nazgul still existed and still were his servants. The fact that the Nine Rings still "worked" would have been the real clue that the One was out there somewhere, and it must be lost but still functioning, since no new Dark Lord had presented herself (or himself).

Incidentally, I don't think that the Nazgul could have ever taken the One. They were slaves to the One (and Sauron) and I doubt that they could have seized it, any more than you or I could grab a piece of lava from Mount Doom and hold it in our hands.

If the Nazgul were capable of seizing the One, then they could have done so on Weathertop. The reason why they instead stabbed Frodo with the Morgul-knife was to turn him into a wraith so that he (still bearing the Ring) could then be brought to Mordor where Sauron would have then taken the Ring from Frodo. Nothing would have given Sauron greater pleasure than to have taken the Ring from its latest bearer. He probably would have simply commanded Frodo to surrender it. Frodo would have been unable to resist Sauron's command even though the psychological/spiritual trauma of doing so would have reduced Frodo to a gibbering insect. The greatest punishment that could have been inflicted upon Frodo would have been to simply allow him to live on in Sauron's shadow, constantly tortured by the sight of the Precious on the Dark Lord's hand. After all, there is such a thing as malice and revenge...