The Ghost of RubangB on 06 November 2008
The Nazgul didn't even know where the ring was. They were all at the front gate to fight Aragorn and all the homies. Instead of Sam and Frodo sneaking in, the eagles could've snuck in right then.
Also, the Nazgul didn't have winged beasts for a really long time. Right after Gandalf killed their horses, the eagles could've busted over immediately.
