When debating online at what point do you agree to disagree?

I’m specifically referring to circumstances when you might be debating a controversial and or political topic with a person and they will just not see reason. No matter matter what you say to them, they will refuse to accept anything contrary to their current frame of thought.

At what point do you give up on taking the debate any further with such people?

This is not directed at any of the Jellies by the way, this is a question I brought up on Yahoo three years ago.