I think we come back to the fact that it's totally reasonable to expect him to see you, but not to make that dependent on coming on a Friday night.
If he's coming for birthdays, Christmas, mother's day and Easter, that's already 18x a year. Add in you visiting them once a month ish and that's 30x a year.
I view myself as really pretty close to my parents, and I probably only see them as much as you're describing. I reckon I see them once every 2 ish weeks on average but is it quite variable. E.g. saw them this weekend (they helped me with DIY), last weekend (mother's day), the weekend before that I'd didn't, the weekend before that we went out, the one before that for a walk, then it was 10 days before that, then I don't think I had seen them for more than a month, looking my calendar. Maybe mum popped in for a cuppa for 20 mins one lunch time but I think I was just busy with other things and they will have been too.
I guess what I'm saying is, I am really very close to my family and I STILL don't think I would meet your expectations of what a son or daughter should be doing.
So you might find you'll be happier if you make a broader friendship group outside family etc so that you're not relying on your family for all your social contact.
I'm not saying don't carry on seeing them as you do now, but I think you have to learn to live with how things are, and expect it may even reduce further as they build their lives. So you need to change your life enough to be happy with the status quo.