You may stop talking to him if he is really serious in his apology he will ask you again to forgive him .
When a person apologizes, he/she might not want to spoil his/her relationship with you, so they apologize for every mistake they made knowingly or unknowingly, but if a person makes a mistake every time and then learns nothing from his mistakes, then to some extent it is appropriate to give them some chances but not again and again. If the same mistake is repeated by the frontman after apologizes, then explain to him that his mistake is making others sad, but even if the person in front is constantly making you upset. So instead of criticizing him in this situation, stop accepting for apologizing and make a distance from him for some time, if you take action in time, then he may really feel his mistake. Meanwhile, focus on your actions, do not waste your time criticizing anyone, just let them learn themselves.
And we have to forget the whole immediately on that moment and never to discuss with others.
At the same time there are people doing the same even after apologized. In such cases we should be very careful.
If a person is doing the same mistake again and again we should tell him and warn him not to repeat. Still, he continues the same mistake we should change his job and put him in another job and give him a chance again.