Leaving aside the quest to destroy the ring; but rather approaching the war from Sauron's perspective: is the winner of the conflict already pretty much guaranteed?
Sauron always assumed that a powerful individual would attempt to claim ownership of the ring to overthrow him. From a game theory point of view this plan seems to have had far greater guarantee of success. The reasons voiced by those powerful enough to achieve this end (such as Gandalf and Galadriel) was that that course of action would replace Sauron with a new dark lord; which, unlike Sauron, had control of the ring and all that that entailed.
So if we are to go with this line of thought Sauron is doomed from the start - very quickly in the narrative his servants fail to prevent the ring from being appropriated by powerful individuals such as Aragorn, Elrond, and Gandalf. While the fellowship's passage east was perilous, such perils were presented by Saruman and the Balrog of Moria, maiar who would likely have claimed the ring had the fellowship been defeated. When eventually Sauron sees Aragorn present himself before the Black Gates with his token force, Sauron assumes that this is the moment of a clash of wills for possession of the ring and bends his entire might (and all of his conscious focus) upon this conflict. Though Aragorn's force was not significant, presumably had Aragorn succeeded in dominating the Ring, it would be game over for Sauron.
Or would it?
Was Sauron guaranteed victory in a struggle (either immediately or ultimately) for control of the ring against an Aragorn or Saruman? We already saw a powerful man (Isildur) claim the ring for himself, with notably poor results. If the odds of such a contest were stacked in Sauron's favour, presumably he had little to fear, and no need to risk much in a war for the ring?
While we (and most of the characters) can only guess at the answer to this - one character who surely would have known the likely winner in such a conflict was Sauron himself. So are his actions one of a desperate player throwing everything he has against the enemy with the world's only super weapon, or dark lord merely killing time before his apparently inevitable success?