You just have to spend ALL your time with Natsuki in all the acts that you get the chance too. Just try and devote all your time to Natsuki. And write all your poems for her too. AND *SPOILERS* she even tries to kiss you at a certain point.
I also got to that point... Natsuki kneels towards you to kiss you but then suddenly Sayori barges in the scene and gets upset without saying much... and shortly afterwards, Sayori hangs herself.
