That's odd. I can assure you that there is no banning going on of any kind, though. Something might be going awry, but the word "banning" can be a sensitive word.
Make sure that they are getting the new invite link from the new game. If that is not working, try sending them a link from a brand new game, just to verify that there is no overall problem. If you want to verify that kicking someone from a game does not disallow them from using a newly generated link, you can create a Dummy Account, invite it (and log in under it), kick it, and then invite it with the new link. It should work fine.
If all this still goes awry, please fill out a Help Center Request, because something is not working properly. Also, please, if you could, report back to this thread regardless. If there is still a problem, I'll do what I can to direct attention to it. If you manage to resolve it, it would be helpful for others to understand what the issue was.