Logical fallacies don't hold up, but they don't disprove an argument either. Just because a fallacy is used doesn't mean the whole argument is automagically bunk. It just means that fallacy can be discounted.
Totally agreed here. Which is why (caveat: depends on which fallacy it is), when I see someone use a fallacy, I usually ask some form of a "why?" question to get them to explain further, or claim I don't understand their argument and ask them to say it a different way, etc, to try to lead them in a direction away from the fallacy. If they're using the fallacy by accident, they usually don't even notice that I'm doing this, and end up making their argument without the fallacy - win on both sides - or they respond in such a way that it becomes obvious to any reader that they don't have any argument at all, at which point it's safe to ignore them.