CatsPhiddle, I agree. It's the same for singing. I read from the paper a few times. After that, I TRY to remember as much as I can without looking at the words.It DOES take practice, and that is what you have to do. It's learning a new skill.
Friends of mine who are in the fiddle camp say that when they go to a workshop, they can easily tell who has been trained classically. Those are the ones who have the hardest time picking up the tune from the ear. You will need to practice listening with the aim to memorizing the tune.
Repetitive listening is my favourite way to learn a song. Do it over, and over and over. Somepeople at the office get right down cranky at me since I listen to a CD, the same CD ALL day or week long. IF I am working on a specific song, I listen to one track continuously, all day, or week long.
It DOES work.