I wish I had a clue of what's going on with those 4 users, sorry If the issue cannot be replicated, it's very hard to diagnose and solve issues.
On the other hand, I have found other problems on your site ... feel free to ignore the rest of this post
Your site doesn't use SSL which these days is very bad practice. A Let's Encrypt certificate is free, there is no excuse not to have one. If your site is hosted on DreamHost, a LE cert is free and very easy to get.
Also, I tried signing up and the captcha doesn't seem to load:
But hitting 'Register' without entering anything brings me to [http://www.animaadoptionagency.com/forum/index.php?action=forum] with no error message... not sure what is supposed to happen next.
When I try to login, I get 'the username doesn't exist'.