No kitchen cabinet coating is going to be as durable as the baked-on factory paint on painted cabinets, and poor preparation or poor quality paint will result in chipping. Preventing paint from chipping off of cabinets isn't easy if the problem is poor adhesion to the cabinet surface. If the problem is poor quality or very old paint, a good sanding followed by primer and two coats of good paint will prevent further chipping.
Buy cabinet door bumper pads and stick them to the corners of doors and drawers to prevent paint chipping when the doors bump onto the frames. These are small cork, vinyl or felt pads and available at hardware stores.
Sand the areas where paint is chipping down to the wood using 100-grit sandpaper. Once they're sanded smooth and feathered out, prime them with two coats of tinted shellac primer. Allow the primer to dry for at least one hour, then touch up with the paint.
Sand entire doors and cabinet boxes if the paint chipping is widespread. Use 80- and 100-grit sandpaper and expect quite a bit of the paint to come off. Use an electric palm sander to make the job go faster. Sand them until the remaining paint is feathered out and smooth.
Clean the surface with a "liquid sander" or deglosser to remove any remaining oils and dirt.
Prime the entire sanded area with oil-based or tinted shellac bonding primer.
Repaint with two coats of high-quality latex or oil-based paint. Use a higher gloss, such as semi-gloss or high-gloss, for maximum durability. The higher the gloss, the harder the paint.