Sauron não podia imaginar que alguém pudesse suportar o poder
É declarado no Conselho de Elrond, como outros métodos de eliminação do anel são levantados, quando Gandalf faz questão de que Sauron nunca pensaria em alguém querendo destruir o anel, por causa do grande poder que possui:
"Into his heart the thought will not enter that any will refuse it, that having the Ring we may seek to destroy it. If we seek this, we shall put him out of reckoning."
The Fellowship of the Ring - The Council of Elrond
E Sauron estava certo: mesmo para Frodo, que havia carregado o anel de inúmeras ligas, a tentação no final era muito grande pouco antes de sua destruição, e sem a ajuda de Gollum, a Irmandade não teria tido sucesso.
Frodo é mostrado ceder à tentação do anel quando se trata de seu obstáculo final, e ele se submete ao seu poder. No entanto, foi sua resiliência inicial e o pensamento equivocado de Sauron que o levou a deixar o Monte Doom sem supervisão.‘I have come,’ [Frodo] said. ‘But I do not choose to do what I came to do. I will not do this deed. The Ring is mine!’ And suddenly, as he set it on his finger, he vanished from Sam’s sight.
The Return of the King
Finalmente, como indicado com excelência por @Pryftan em seu resposta encontrada aqui , Tolkien escreve, na famosa Carta 131, que Sauron não precisava usar o anel para manter seu poder a menos que fosse reivindicado por outra pessoa. Continua descrevendo como ele estava convencido de que ninguém poderia destruir o anel antes de sucumbir a ele. (O que mostramos acima é verdade).
But to achieve this he had been obliged to let a great part of his own inherent power (a frequent and very significant motive in myth and fairy-story) pass into the One Ring. While he wore it, his power on earth was actually enhanced. But even if he did not wear it, that power existed and was in 'rapport' with himself: he was not 'diminished'. Unless some other seized it and became possessed of it. If that happened, the new possessor could (if sufficiently strong and heroic by nature) challenge Sauron, become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place. This was the essential weakness he had introduced into his situation in his effort (largely unsuccessful) to enslave the Elves, and his desire to establish control over the minds and wills of his servants. There was another weakness: if the One Ring was actually unmade, annihilated, then its power would be dissolved, Sauron's own being would be diminished to vanishing point, and he would be reduced to a shadow, a mere memory of malicious will. But that he never contemplated nor feared. The Ring was unbreakable by any smithcraft less than his own. It was indissoluble in any fire, save the undying subterranean fire where it was made - and that was unapproachable, in Mordor. Also so great was the Ring's power of lust, that anyone who used it became mastered by it; it was beyond the strength of any will (even his own) to injure it, cast it away, or neglect it. So he thought. It was in any case on his finger.
The Letter of J.R.R. Tolkien - Letter 131, to Milton Waldman
Tolkien claramente descreve que Sauron foi incapaz de perceber que alguém passaria por Mordor, subindo ao lado de Orodruin e entrando no Sammath Naur sem ter cedido às tentações do anel. Isto é mais provável porque ele nunca conheceu Hobbits nem foi capaz de prever sua falta de desejo por poder e seu conteúdo por uma vida simples.
Novamente, como afirma @Pryftan, especula-se que o "deslize" de Gollum foi uma das interrupções de Eru Iluvatar (o Todo Poderoso) na série que acabou destruindo o Um Anel.