How to help my son?

My sons father walked away after a 4 year relationship when I got pregnant. He didn't want anything to do with me or his child. When my son turned 3, he decided he wanted to be in his life and I let him, few months later he cut contact again. 2 years later he asked for contact again and I said yes, again this lasted a few months and he just stopped talking to us again. Another two years went by and I thought he matured, realised the mistake he made and would step up. He started seeing his son again when the child was 7, they had an ok relationship but this lasted a few months and he cut contact again. I tried so hard to keep him around, I begged him to just be there for his son but he'd ignore me and eventually blocked me. I told him his son was old enough now to understand and see what's happening and that he cannot keep playing with his feelings like that. It's been 2 years and this has really affected my son. He's 9 years old now and often questions why his dad isn't around, to make things worse, some kids at school started bullying him saying he's "fatherless" I can tell it really gets to him and I have no idea what to do. He has recently been diagnosed with ADHD and I can't stop blaming myself, I feel like I'm the cause of this because he's been through so much rejection in life. I hate myself and I feel like the worst mother in the world, watching him get angry and then cry that he doesn't even have a dad. Please help me, what do I do to make him feel better? And how do I stop hating myself for allowing this man to do this to us? How do I make my son happy on my own? I'm really struggling, and so is he, please help.