As your points get used and wear, they get pits in them. The spark jumps between the pits so that is the actual gap now. You can't measure between the pits with a feeler gauge. The setting you think you're getting is actually larger because you're using the gap you have between the pits. The only accurate way to set used points is with a dwell meter. That reads the actual point gap electronically.
Usually, points should be good for 15K miles or so. After that, even if the surfaces are not badly worn, the spring steel strip that forces them closed could be getting weak. In that amount of miles, the points open and close literally millions of times, so it's a good idea to replace them every 15 to 20K.