Am guilty i must confess. Guilty of what you might ask? Well, you asked how long to work and wait in anticipation of that "yes" you so desire to hear from someone you"re willing to give your commitment, emotionally, right?
Those weren't the exact words you used, but it is at least exactly the way i felt before putting in two years in the pursuit of love, that was my first relationship and gosh! I was in love. It didn't matter the amount of effort and how long it took for her to come around the idea, all that was of concern to me was getting that opportunity to continually express my undying love for her. Unfortunately, it ended a while ago. I still have some certain amount of feelings for her in a way a brother does even though we're continents apart.
Just like @greencrayon stated below, there's no defined or predetermined length of time expected of a person to put in effort in the pursuance of the one they love. It is of your personality. Regardless of their feelings, some folks lack the patience, some have egos and some might just have a certain feeling of embarrassment everytime they get turned down. It is only normal for people of such personality to back down in such situations.
Anyways, love is not a feeling that sparks at first contact, it is a process, an act of true emotional expression that needs to be found, built from within the heart, nurtured and maintained in the best way possible. In saying so, time shouldn't in anyway stand as a draw back when seeking a yes from that person who grips your heart as feelings grow stronger by each passing moment.