I knew a guy who had a clear "three strikes rule". If you turned down invitations three times in a row, you were told clearly that you weren't getting any more invites until you had extended one yourself. It's pretty fair.
These days I know a lot of busy people, so my softer version is, if I invite you to a thing and three times in a row you don't even reply, I'll probably just quietly stop inviting you altogether. I'm ok to keep you on the list if you make the effort to reply and explain why you can't come.
You bringing in the "three strikes rule", I'm reminded of game theory.
They have the famous (repeat) prisoner's game, where two parties decide to either collaborate or to screw the other party. People ran software simulations of various strategies, and the winner is: Tit for tat. In other words, you start positive (invite), and stay like that until the other person screws you. They you screw them once next time and turn collaborative again immediately after (no hard feelings).
I'm not advocating you play the prisoner's game on people, but it's interesting that people worked formally on something relating to this.
AFAIK the strategy was slightly different: You start collaborative, and then simply repeat the other person's last action. This means that, if they screw you, you keep screwing them until they turn collaborative, at which point you collaborate in the next iteration.
Yup. In real situations, one element is that sometimes things are misunderstood, and in particular sometimes collaborating is mistaken for defecting, so if all sides are playing pure tit-for-tat, then one can end up in a defect-defect loop forever (or, I guess, until the opposite misinterpretation occurs). Therefore, an element of forgiveness (some percent chance that you'll respond to a defect with a cooperate) can be helpful.
These days I know a lot of busy people, so my softer version is, if I invite you to a thing and three times in a row you don't even reply, I'll probably just quietly stop inviting you altogether. I'm ok to keep you on the list if you make the effort to reply and explain why you can't come.