Sometimes in order to become a better composer, you have to spend more time listening to good music than you do composing - just so long as you're "listening" to the music, absorbing what you're hearing, and applying it, and not just enjoying the music. For this reason, I don't think you can seperate the process of listening to music to the process of writing it too much.
Some songs do have a mind of their own. They don't always want to be finished right away. I've revisited material that I originally wrote nearly half a decade ago before. Its only when you try to force it does bad material happen, and it's not worth writing bad material just so you can get pieces done sooner.