Hi there Marisa,
There is one reason why an invite wouldn't go through, it's if the email is already in the system. But, I do believe there is an issue with invites, and have put it back on my test list.
In the meantime, you could just send a direct email with a link to your forum because that is all the invite does anyway, it sends a link.
Now for the profile you invited, it will now show the communities until you've made a post. After you make your first post, the community will show.