If you honestly believe he has changed then trust yourself, but if there is any doubt I would say leave him. I may not be the most reliable person, but I can see why you seek help. I hope this avails you.
You can continue to teach him that he can always run back to you as a last resort, or you can teach him that you don't wait for people who have no idea of what they want. Past behavior is the best way to judge future behavior.
It takes more than months to change sometimes they never change. Guys lie to get what they want and there good at it. If he already cheated on you 3 times he doesn't take you seriously and probably never will. It's probably best if you move on cause obviously he did after the first time he cheated