Usually we see one extreme or the other.
Some concrete curbs hold paint well while others are chronic peelers.
Concrete takes 28 days to reach full hardness, and can give off dust for another 6 months after that. Therefore curbs must be allowed to fully cure before paint is applied.
Notice that if there are several layers on the curb, generally they all come off at once. Therefore the problem is not with the most painting job, but with the original one.
One solution is to sand blast or water blast all of the paint off the curb back to original concrete. Then we can repaint the entire curb with an oil base paint which will stand the test of time. This is a fairly expensive option.