From my experience, dropping the rope is both a conscious and unconscious decision and action...
It comes from detachment and my opinion is, the only way you really do end up dropping the rope in any significant way is when you become detached enough that you truly are living your life for you...
"Thought stopping" is a term used to help promote detachment... if you are having morose thoughts or are thinking about your H a lot... have something that you can focus your attention on... DO something to take your mind off it...
