Ideally, you want to adjust the door so that no painted surfaces are ever touching each other. I realize this isn't always possible, but if the door closes and the surfaces are pressed together hard or rubbing, this is always going to be a problem. You may also be able to sand the door or the frame or both until the painted surfaces are not rubbing. Once you have the areas sanded down, you want to spot prime with some primer that is good at bonding and then touch up the door and frame with the paint. Latex paint will take up to a month to cure, and the paint will stick less when it is fully cured.