So he's basically saying "You're right, you can't trust me. But trust me anyway."
I'm with Jayne. Trust is a privilege, not a right. You can lose privileges by abusing them.
The onus is on him to prove that he's trustworthy. He has to show clear signs of improvement. Rule number 1: Never trust someone who says "trust me." It's dangerous that you want to trust him, because that will make you more likely to do so before he's actually earned it.
One way he can show that he's trustworthy is to temporarily agree to more stringent rules than before. Without details, I can't be more specific. He can show that he's willing to go above and beyond, putting his own comfort and desires on hold for a while to show that he's committed to earning your trust. That's a lot more evidence than his word, which has been proven to be meaningless.
I would also discuss why he broke the rule. Was it a rule that he was never really comfortable with in the first place, but he agreed to because he felt that he had no choice? Then he needs to learn to be honest and assertive. If you make a request that he just can't follow, he needs to tell you up front that it's not going to work.
The threat of you leaving if he does it again probably won't cut it. That will only motivate him not to get caught. If he's not genuinely committed to being worthy of your trust, then no threats or promises are going to change that.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker