If a reasonable person were to read your discussion and see the falsity of the other debaters' argument, you've succeeded.
If they were to read your discussion and see the truth of your argument, you've succeeded.
If, through having a discussion, you see the falsity of your own argument (and you admit it), you can abandon the discussion with your dignity intact.
How convinced or otherwise an irrational debater is by your argument is irrelevant. However, there is no time when saying 'we're done here' casts you in a good light.
If they were to read your discussion and see the truth of your argument, you've succeeded.
If, through having a discussion, you see the falsity of your own argument (and you admit it), you can abandon the discussion with your dignity intact.
How convinced or otherwise an irrational debater is by your argument is irrelevant. However, there is no time when saying 'we're done here' casts you in a good light.