Imagine that someone you know has a reaction that you consider disproportionate to the severity of the event that caused it. If your friend loses their comb, and they get weirdly angry about it, and you persuade them into calming down with rational argument, and then it happens again, say, many months later, and they get just as angry as they did the first time, is that person unteachable? Is it a waste of your time to try to persuade them using rationality?

There are two ways you can interpret rationality in that sentence:
(1) Appeal to explicit reasoning by providing objectively true arguments why being angry doesn't make sense.
(2) Appeal to effective actions.

Don't confuse the two. They are very different in this case. The kind of rational persuasion that Jimmy with his hypnosis background talks isn't simply just providing objectively true information.

At the beginning of the last LW Europe Community Camp we went out bouldering. There was a girl who at the beginning had a phobia of heights that prevented her from going on a slackline. Two hours later she didn't have the phobia anymore, and found that highly surprising. She also had a public speaking phobia and gave half a year later a talk in front of 1000 people.

As far as amnesia goes, amnesia isn't a problem. In hypnosis amensia sometimes even get's consciously added. If you actually remove the emotional attachment that produced the problem it doesn't matter whether they remember the conversation the next time the friend loses their comb.