Although it appears to be hard and solid, concrete is actually a porous aggregate of cement, sand, moisture and minerals. Extreme weather can cause concrete garage floors to chip and crack, not to mention the abuse that cars cause as they're repeatedly driven across the surface, some dripping oils. Concrete sealers work to protect the surface of concrete but they can also prevent paint absorption. Unsealed concrete can cause paint to peel as well, since moisture evaporating from the concrete prevents paint from adhering to its surface.
Garage floors require a type of paint that is hard and durable enough to stand up to both foot traffic and the weight of cars. Many paint manufacturers offer a high-performance paint specifically made for garage floors. Elastomeric epoxy paint is a thick paint that seeps into small cracks and pits and forms a strong bond with concrete.
Remove the peeling paint on the garage floor so you can properly prepare the surface. Use a wide scraper to remove loose peeling paint and any efflorescence, a white substance that appears as moisture evaporates from concrete. Then use a grinder or chemical stripper to remove all old paint and sealer.
After removing the peeling paint, sweep and hose down or power wash the garage floor to remove all dirt and debris. Apply a strong detergent solution or commercial degreaser to remove any oils from the surface. Rinse and allow the floor to dry for several days. Apply muriatic acid to etch the concrete, creating a rough surface that will bond well with primer and paint. Wear protective gear, and use and store the acid according to the manufacturer's directions. When the surface dries, apply a high-quality primer to the garage floor and allow it to dry for the amount of time recommended by the manufacturer. Then paint the floor with epoxy paint. Wait at least 24 hours before returning stored items to the garage and at least a week before parking cars.