: : : : Gandalf

: : : You're missing the point. The Silmarils did not fade with Feanor's death, BUT, if he had allowed the Valar to use them to resurrect the Trees, (destroying them in the process) he could not have created new ones.

: : : It was not the downfall of Sauron that caused the Three to fade, but the destruction of the One. Sauron used a great deal of his power to tie the Three, the Seven, and the Nine to the One. The destruction of the One caused Sauron's downfall, as well as the downfall of anything connected to it. New Rings could not be made for the same reason that new Silmarils could not be made.

: : How's this for an analogy:
: : I offer people a machine that will provide electricity to their homes at no cost. Unknown to those people I make a machine that allows me to take not only total control the their machines, but also control every electical device in their home. Three of the people discover this and immediately disconnect their machines. They reconnect and use their machines only when they know I am no where near my machine. My machine is destroyed, none of their machines no longer work, and I am killed because my machine also powered my pace-maker.

: Nope, doesn't work...
: Sauron had much to do with the physics of the rings, but gravity will hardly shut off if Newton dies! He may have discovered the way to channel the powers into rings, but i doubt if all ring lore will die just because Sauron does.

: Gandalf

Simply put, the One Ring was the link between the other rings and the lore. When the One was destroyed, the link was broken.
The lore still existed but could not connect with the other rings.