Thanks Dennis P.
Aaron B.

In response to my question, a few people have repeated the explanations given in the book by Gandalf and others. It still seems hard to believe that retreating was the best choice for the Nazgul, when they had Frodo surrounded at night in the wilderness with nothing but Aragorn's flaming brand and the name of "Elbereth" to stop them.

Dennis P., you have offered an interesting theory, that the Nazgul were reluctant to finish the job at Weathertop because Frodo could potentially have mastered them if he donned the One Ring.

Why, then, would Aragorn counsel Frodo that the name of Elbereth, rather than wearing the Ring, was more dangerous to the Nazgul? And didn't Gandalf say that putting on the Ring was a bad idea, because it put Frodo in the shadow world and made him more vulnerable?

Building on Dennis P.'s theory, note that Gandalf mentions in his explanation that the Nazgul at Weathertop were without their leader, the Witch-King. Perhaps the Witch-King was concerned that one of his Nazgul lackeys would get the Ring and seek to supplant the Witch-King as Sauron's right-hand man? Maybe the Witch-King, through the force of his will and some nefarious telepathic power, caused the Nazgul to retreat, until he could get to the action and win the Ring for himself.