|The LOTR Movie Site
March 1, 2001
Edmund and Stephanie, Regarding
Regarding the Nazgul, and their reluctance to persue Frodo after he put on the ring, they feared the power he could wield. The ring wasn't simply a "ring of invisibility," it was THE ring of power. When Sauron created the One Ring, he imbued it with a major portion of his essence and power. The Nazgul, by this stage, owed their very existence to the ring. The ring gave shape to their forms and allowed them to remain in Middle Earth even though their time had passed.
What they feared, I believe, is that Frodo, in his fear, could very well command or wish them to cease to exist. Instead of pushing Frodo to this point, they withdrew. They had hoped to catch him before he donned the ring. That is the reason for the second attack at the fords. When they tried to ambush the hobbit party at the fords, Frodo had removed the ring and was again vulnerable.
After these two attacks, Tolkien has them abandon their efforts at recovering the ring. Instead, they focus their efforts on the upcoming war and wait until perhaps another ringbearer, who is more reluctant to don the ring, comes into its possession.