Chinfan, as long as the paint is adhered to the surface, there's no sense removing it only to apply more. In the absence of moisture coming through the back/underside, and with the original paint applied to a stable surface, concrete holds paint pretty well. After washing, be sure to allow ample drying time, it holds moisture well also. I'm not sure how long, but two good drying days should do. Also be sure to check whether your finish is spec'd to go straight over bare concrete, some are and others aren't. Or, if you think you may have trouble, consider using SW Loxon concrete primer. It may not be necessary, but it'll never hurt (unless you're using Drylock).