Question

Why does Wiesel vow never to do in this Nobel Prize acceptance speech?

Answer 1

Because he wants nobody to be silent about issues in the real world, he wants them to be heard .
or 
to never be silent.

Answer 2

If we're talking about the same Wiesel, (in this case I'm talking about the one that created the book "Night") then he did do the acceptance speech. However, he did say in the speech, that he would not accept the nobel prize on behalf of the people who died on WWII, because no one has a right to speak for the dead.