[Belegorn]

If Frodo died, or lost the Ring to Sauron I do not think Gandalf would have given up. Obviously things would certainly be different and very nearly was. The Nazgûl would be infinitely stronger, "they are only shadows yet of the power and terror they would possess if the Ruling Ring was on their master's hand again" [FotR, A Journey in the Dark] and Sauron would as Gandalf told Frodo have "strength and knowledge to beat down all resistance, break the last defenses, and cover all the lands in a second darkness." [The Shadow of the Past] It would be very tough, however, especially with the Elvish strongholds held by the bearers of the Three since "all that has been wrought with them will be laid bare, and he will be stronger than ever." The One was really malicious when you think about it in terms of it's connection with the other Rings in seeing their workings and the minds of their bearers.