I've accepted a game invite and nothing happens for a long time. The game I was invited to was likely over. Later when that player starts a new game the one who was invited could get snatched out of the game they were playing to find themselves in a lobby. It's happened to me and it's happened to people I know. I assume that Uber knows about this and a fix is in the works, but I am asking players not to use game invites while this problem can still occur. If you can send them game invites then you can send them messages instead. This is my point of view and I may be somewhat uninformed. Feel free to correct me or offer a differing point of view.
if the game you are invited to is set to private nothing happens too. However what you describe sounds like a bug where the invite is not specific to the game it was send from
