The heart of it is how the song makes you feel. The emotional response you have to it whether you have heard it once, twice or repeatedly over the decades.
And I believe that a large part of your response is in response to how much of their soul the performers put into the version that you fell for. Just today I listened to a live version, by the original artist, of a song that elicits that emotional response from me and it was not the same. It just didn’t hold me. I think the live performance was listless and being done by rote. Of course, I can’t blame the artists. It must be difficult to put into a song you have performed 100 times the same energy and spirit that you put into the first few playings. I looked up the original and listened to it and was glad to find that I still had the emotional connection to it in its original form.
Another part of it is that the song has to stand out of the crowd. It has to have a hook that grabs you. How many can tell Freebird or Hotel California by the first few notes? In both these particular cases it is the guitar work that renders them classics, at least in my opinion. What about Beethoven’s 5th? Or Wagners Ride of the Valkyries, not to mention Bachs Toccata & Fugue in D Minor. Again, all easily recognizable in the first few notes. And who does not recognize the crashing cymbals that signify the beginning of O Fortuna from Orffs Carmina Burana.