There is no reason to "debate" an atheist. They hear the Word or they don't.
This is a good point, although a hard one to hear. It goes completely against our nature and popular American church culture.
Back in the days when I would frequently encounter Mormons, I would enter into dialogue with them. We would talk about various issues and beliefs, and I could easily "win" the debate because I was quite familiar with their scriptures and practice, and I also knew the Bible. Many times when we were discussing various Mormon claims vs. the claims of Jesus and the scripture, I would clearly demonstrate that the Mormons were wrong - even to the point that the Mormons I was speaking with conceded that it sure looked like I was correct. I even had two Mormon missionaries unable to properly respond to issues with their scriptures and the false claims of Joseph Smith. In my way of thinking, that should have meant that they would automatically become Christians.
However, it is much easier to make a Mormon an atheist than to lead one to Christ, simply because you can engage a Mormon on the level of reason - and devastate their belief system - but you can't give them God-given faith.
In a similar way, you can prove an atheist to be in error (although that is much harder, since unbelief takes no real intelligence or defense) and they may still persist in their unbelief because they do not have God-given faith. They will just develop new arguments.
Beyond all of that, even if a person is open to faith, a debate/argument involves the ego and they will want to "win" the argument so that they will not have to admit they are wrong. You could demonstrate something conclusively, but they will decide to continue to embrace a false view simply for the sake of their ego. (Psst! That happens a lot here.)
When the Spirit is working with you and you enter into a discussion with someone of another faith or an atheistic faith, you can afford to be humble, patient and risk "losing" an argument if they happen to find an area of ignorance or inconsistency on your side. Since the results do not depend on you, you don't have to "win." You also can set the tone for the discussion to avoid letting egos get in the way. On more than a few occasions, when things started to get passionate, I have come right out and stated that I have no interesting in continuing the discussion since I value my relationship with the person more than winning an argument. Every time I have done that, the tone immediately shifted to a more respectful and calm level and we continued talking about the subject in an honest and comfortable way. The Spirit honors that humility, and I have seen a modest number come to faith. And I know the Spirit is working with others who are not yet at the point where faith begins to appear, but the seeds are sown and are germinating.