If you can persuade me that you're willing to make a proper contribution to this debate, I will lift the ban I've just placed.

Why does someone else have to prove to you they can make a proper contribution to the debate. Who do you think you are placing a ban on someone, and then they have to justify to you they can make good contributions to any debates. You're not the judge, you're not the be all and end all of their actions and decisions.

What if the person doesn't know how to argue according to the level of logic you use to make your arguments, what if the person is just learning how to argue, and because of you, you are preventing them from honing out their skills to become an effective critical thinker? We all must persevere with people lesser than ourselves just like people better than us have to persevere with us.

If you don't like someone elses reply to your argument, and their argument is nonsense, tell them it's nonsense but don't ban them. You will do more for them using criticism than you would banning them.