In Elie Wiesel's speech "The Perils of Indifference," one of the speaker's purposes seems to be to encourage the audience to prevent negative events in the past from being repeated in the future. Does Wiesel effectively convince his audience to keep history from repeating itself? Why or why not?

I am a great admirer of Elie Wiesel, and I mourn his passing.  His mission was just and his work was important.  He turned his loss and pain into a force for good.  My father liberated a concentration camp. I am Jewish. I share these facts to show that if I had a tendency to be biased about Wiesel's speech, it would be a bias for it, not against it. However, I do not think that this particular speech was effective in its effort to convince us to remember the past to prevent further genocides.
Much of what Wiesel did in this speech was to accuse the world of indifference, most particularly the United States.  He pointed out specific instances of American indifference to the plight of the Jews in Europe. And everything he had to say was factual and justified. 
The problem is, though, I don't think it was necessarily persuasive, at least not to an American audience. I do think this has to do with the American character, which responds best to rhetorical flights of fancy word work, loads of optimism, and ample praise. I suspect many an American tuned him out once he stopped thanking us for rescuing him.  It is a dry speech, really, and Night is far more persuasive a text because it is easier to feel empathy for one person than for six million. 
Honestly, I do not know how we persuade people in the world to remember and not repeat these horrific genocides. So many people seem to want to forget, and there is that whole subset of people who insist the Holocaust never even happened.  Soon, most survivors of the Holocaust will be gone, and it is clear today that a substantial number of people remain indifferent, to women, to LGBTGs, to immigrants, to African-Americans, to the poor. I hope that the up and coming generation is motivated somehow to take a "Never Again" stance.