I've been experiencing some problems with the publishing feature lately.
I add a new website, try to publish my project, and get the message "Couldn't publish your website, please try again later" (no more informations in the console).
If I hit cancel and try to publish again later, the website has disappeared and I have to create it again.
More troublesome: yesterday, it worked, my last designs where online, but today the website has disappeared.
Sorry that you've run into problems! Has the "Delete After" option been set when the website was created by any chance? If you wish to keep your site online indefinitely, you need to set it to "Never". Otherwise it is deleted automatically after the set period ends.
It turns out there was a bug with our new publish functionality. This is now fixed and you should be able to create websites without issues. Sorry for the trouble!