The relationship between Saurons spirit and the One

In "The Shadow of the Past", Gandalf speculates that Sauron himself believed that the ring had "perished", but "now" knows that it indeed was intact: ‘And this is the dreadful chance, Frodo. He believed that the One had perished; that the Elves had destroyed it, as should have been done. But he knows now that it has not perished, that it has been found. So he is seeking it, seeking it, and all his thought is bent on it. It is his great hope and our great fear.’

Gandalf later seems to be confident that the destruction of the Ring would be the final defeat of Sauron.

We also get a glimpse of the omniscient author when we are told of Saurons reaction to Frodo claiming the Ring in the Sammath Naur (unless this is supposed to be a projection or speculation of Frodos). Sauron was supposedly aware of the magnitude of his danger, the Ring being so close to potential destruction.

What do you make of this? Wouldn´t Sauron at all times know wether the Ring was destroyed? Could Gandalf mean that Sauron simply believed the Ring to be "lost forever", like Saruman tried to convince the White Council it was? Perhaps Saurons spirit was so weak after his "death" at the hands of the Alliance leaders, that he the following years couldn´t tell wether the ring was destroyed or not, as he himself was indistinguishable from the form he would take if the ring was indeed destroyed?