this reminds me of a friend who we've excluded from the group b/c of the age old advice of "the worst they can say is no". Well, we invited him to everything at first it was either no responses or late responses like "sorry was busy with work". The whole friend group took their turns and attempts at inviting him. It sort of stopped altogether when we started getting responses like "hey, don't call me without scheduli…
Anna in the story did not express regret that she never joined. And as far as we know, Alexei wasn't expecting her to take his invitations either - because it wasn't about actually getting her to go to the party, it was just about communicating to her that the "we've stopped inviting you to our group events because you always say no" moment never happened and she was still a part of the group. That was what she had appreciated in the end.
On the other hand, what your group attempted seems more like a concerted push to change the person's behavior. Most people would probably reject that if they want to stay in control of their own plans.