Why would he talk to me everyday on Skype when we're no longer together?

My ex broke up a month with me a month ago and he’s been initiating online conversations with me every day since. He always says ‘I hope you’re okay’ and is very apologetic when he takes a while to respond.

A few people have said he just feels guilty about ending things. It’s true that I was very upset about the break up at first, but that eventually passed. Since then I’ve always been positive and friendly to him and told him I’m doing fine, so there is no need for him to feel guilty. He seems happy/relieved when I tell him this and says I’m incredible. However, me explaining that I’m fine still doesn’t stop him saying “I hope you’re okay” all the time.

Since the break up, I’ve only initiated once. When I did, he thanked me for saying hi and said it meant a lot to him, and told me to please stay awesome and amazing. I’m simply wondering what could be on his mind. I don’t wish to ask him as I don’t want to be confrontational or make him assume I want him back.

P.S. We were in a relationship for 3 years and knew each other for many many years before that, so please don’t tell me to block him. :) I’m not hurting and don’t wish to remove an important person from my life. Just because he was the dumper doesn’t mean he is a bad person. It was my depression and anxiety that caused the strain on our relationship and I hold no resentments towards him.