The Nazgul were probably busy fighting the rest of the army, remember, Sauron came out to fight after about a month of the siege of Barad-Dur, the Nazgul could have been defeated during the battle of Dagorlad as well.
Keep in mind, after Narsil was shattered, it was reforged into Anduril by Elvish smiths, so it had Dwarvish and Elvish smithing techniques, which may have made the blade weaker due to illregualrity in the techniques.
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