Want him back, still living together

Boyfriend recently broke up with me over resentment. He says he still cares and loves me. I’m taking this extremely hard. I want him back and I want him to see I’ve changed. It’s been about 3 years and our first year was really tough and he still hasn’t forgiven me. It’s only been four days and he’s already chatting up other girls he says it’s just a distraction to avoid falling back to me. I’m just sad and I really believe he is the love of my life. Im giving him the space and time and hoping for a change of mind from him. I figure if I continue to show that I’m different now he can come around to truly forgiving me. I know it might just be over but he’s autistic so it does take him longer to get over things than the average person. I just love him and am not ready to fully close the door on us.