The familiarization process discussed here with music, reminds me of my own experiences; one of which deals with John Coltrane. I remember the first time I listened to Coltrane's "A Love Supreme". I could barely concentrate. It was so hard for me to remain in the moment in a participatory way; therefore, the music sounded rather "bizarre" to my mind’s ear. One day, all of that changed, and now, whenever I listen to any Coltrane, I hear it all with ease, and I seem to have become an addict. My transaction with his music comes easily now.
I believe that with good poetry, there is also this same sort of "learning curve" that is trekked by repetitive (and I believe, leisurely) readings. It is an assimilation process, a cultivation of the mind, and I believe that we all have our own individual levels as to how long this process will take. It's like taking flying lessons, where at the beginning, there is marginal perception of depth, speed, altitude, attitude, etc. It doesn't necessarily happen over night (at least in the beginning stages). This also goes back to what Kasey talked about a few years ago regarding "poetic transmission." The poem opens up like a flower (in its own time) and becomes accessible. This is a kind of subconscious or unconscious activity, and I believe, it becomes a skill.
Once this is experienced, whether poetry or music, and it becomes accessible; it is all that much more enjoyable--and it is enjoyable longer, and therefore I think, "classic."
(and of course the context, and not just "a" poem is very important, as pointed out quite well here)