I feel that it would be terribly sad if all music faded or died after the original performance. Personally, I think every performance or rendition of a song has the potential to be better than the first; I don't see anything magical about the first effort, and indeed many songs have benefited from a revisit by the original artist.
To list examples of songs where I believe a cover, re-recording or live performance is better would be pointless as it's entirely subjective. In many cases - where a song switches genre, for example, it's greatly influenced by social and cultural factors.