Should I let my friendship with my best friend of almost three years have a "natural" fall-out or no?

My opinion is that you are right to let it cool down if that is what she wants, her comments to you in the past puts me in mind of someone I knew who found out far too late what her "girlfriend" thought of his judgment although I know for a fact that he almost run himself into the ground trying to give her all she wanted, all she did was find fault, and bring up things that had happened years before. I was helping to build a new wing on their house, and the only comment I heard was"I told you it wasn't big enough". never a word of thanks. Stay clear, hope you meet a more agreeable girl friend.