I'll go against the grain here. If I invite someone a couple of times, and constantly get declined no way I'll invite that person anymore, because I make an effort to invite you. Declining (repeatedly) makes me feel like an ass for inviting you. And I want friends that respond, not friends that reject me. Wanting to be invited just to decline sounds.. egotistical to me. A relationship is a two way street, and being that shy is a you problem.

To even be more cynical, maybe Alexei wanted something more from Anna? Because I certainly haven't seen people invite someone to repeatedly get declined.