You have made it clear to him that you will NO longer put up with his comments! If it were me I would be " too busy with life" to Skype him.

Maybe just send few quick email responses to him. " Sorry we haven't been in touch much but I am very busy with work and social events"

But hey that's just me and I can be a "Snarly female dog" at times
I have ZERO tolerance for ignorance!