There is perhaps nothing more annoying than someone who is persistent and simply won’t leave you alone. Many children seem to have this trait, as when they see something they really want, they will stop at nothing in trying to convince the parent to purchase it.
In terms of someone harassing you or even worse, bullying, then there is a limit to how much one can tolerate. If the person is persistent in their efforts, there will eventually be a point where we reach that causes us to take action to the next level. For example, instead of walking away, one may attack the bully instead.