I recall one time - years ago - where a poster was repeatedly insisting in a same sex marriage thread that there was a possibility he could marry his dishwasher. He didn’t respond to refutations but returned to that point often enough that I told him it was out of bounds and if I saw him again he would be warned.
But note; that’s debating in bad faith.
That did not actually happen and you are misrepresenting that poster.
The poster didn’t argue that he could marry his dishwasher. He argued that the same arguments which were being used to require recognition of SSM should also logically be used to require recognition of marriage to inanimate objects such as dishwashers, to people who felt that way.
What happened wasn’t that he “didn’t respond to refutations”; he actually responded repeatedly and at length. Rather, what happened is that many posters who were strongly in favor of SSM objected to the notion that this could be compared to marrying dishwashers, and declared that their counterarguments amounted to refutations that the poster had failed to acknowledge. It’s frequently the case that people believe they’ve “refuted” their debate opponents while the debate opponents disagree with this, but in this case, those maintaining that view had the majority on their side and sympathetic moderation.
The point of all this is that an assessment whether someone is “debating in good faith” can be highly subjective, and is highly dependent on one’s view of the underlying issue.
[For some reason I can’t link to the original thread - there’s a follow-up thread here but the link to the original doesn’t work.]