An intriguing question. I've found that if I really can't relate to music on the first try, it generally doesn't get better on repeats. The fascinating part is that some of my favorite music started out as borderline on the first play. That is, it sounded OK but not great on the first try, then it grew on me. Examples include St. Germain (techno/jazz), Eva Cassidy (female vocal jazz), and Hugh Masekala (jazz with African themes), versus my nominal preferences for classical and smooth jazz. But the stuff that was far away to begin with, like FIM's Chinese instrumentals or very abstract jazz, never got closer.
I don't understand music in the way that musicians seem to. I don't have an appreciation for the detail and choices involved in the composition and performance. All I generally hear is the overall sound, the tone and direction of the music. I don't usually follow the play of individual instruments in a group performance. Maybe that's why good sound reproduction is more important to me than to a musician, who could get off on the artistry of what the musicians are doing rather than the overall effect. Somebody like that could be more appreciative of the stuff I can't relate to.