The Dwarves were already seemingly on the edge of demographic decline owing to the small number of dwarven women, so it wouldn't have taken much to push them over.
In the case of the Khazad and the Quendi, I guess I'd call it a loss-of-habitat crisis, both physically and spiritually. The general preserving strength of Elven "magic" would have declined sharply after the One's destruction took away the power of the Three, and Moria remained lost even if Gimli made a new home in Aglarond.
And the fading wasn't limited to the Elves and Dwarves... after the throwback of Elessar's lifespan, the Kings went back to their decline from Numenorean to ordinary human vitality.
Actually, the dwarves could still be there underground, and hobbits hiding in the woods...