When I am trying to persuade someone of something, it can be tempting to think of clever arguments to intellectually refute their points. Sometimes, people eventually acknowledge that 'you win', and they can't think of any good response/defense.
I consider this a loss.
If they seem disappointed, defensive, or down-trodden, they likely haven't been convinced on a System 1 level, even if their System 2 can't think of any further reasons why you're wrong.
I guess this might be ok if your primary target is those observing the discussion. But if you don't convince them on a System 1 level, all that happens is you win the conversation, and they go on with their life exactly as before.
If you can convince them on a [[System 1 and System 2|System 1]] level by really, really understanding their models and illustrating whether crux of the disagreement lies, they will internalize the new belief, change their behavior, and become a spokesperson for the new belief.
If you can't do that, you may need to more fully internalize their objections, and consider whether you are the one who should update their beliefs.