We check this website, now thinkbabynames.com is up and dont blocked for our system and other users of the Internet.
So, answer to question: Is thinkbabynames Down Right Now? - NO! thinkbabynames is up!
If you have problem with access to site thinkbabynames, and domain thinkbabynames.com is not avalible.
Clear browser cache and/or try other web browser
(Chrome, Firefox or Safari).