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