This won't happen again. I promise.
It can't happen.
What does the change of the auxiliary verb mean?
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Won't implies either a pledge, as in your example (I promise), or a confident prediction, or a refusal:
Abduction by Martians has dropped off since the 70s. I'm pretty sure it won't happen to you again.
No matter how much you offer I won't sell you my daughter.
Can't implies either an impossibility or a directive:
I'm sorry Bobby made that rude gesture. It can't happen again, because we've cut off his hands.
Yesterday Cathy sold one customer another customer's umbrella. This can't happen again.