Whatever I paint with latex ends up sticking. Maybe it's the humid summers or how I apply it, but the glossier the finish the more things stick. I've given up on latex for doors, windows, shelves, etc. My advice... go with oil.
You have to be careful with water based paint on doors due to the sticking issues. Even 100% acrylic house paints can have issues. Higher grade products like Duration, Accolade, Aura, etc. have a different kind of acrylic resin in them and cure harder, which avoids the sticking problem.