I was wrong, it actually isn't that low..To be clear, phpBB did not shut down your site.
Why you're seeing the error message in phpBB is because phpBB is connecting to your database server, and the database server is returning the error message that the limit of connections is reached. So phpBB only displays the error that it gets from the database server as the database won't give it the data it expects.
So this error message is caused by the limit on the database server and not by phpBB which, as noted in the topic, is set quite low by your host.
And there was not a sudden surge two days ago that would have caused this..
I upgraded, so by the end of the day I should know if that will work..
It just seems so strange, a very small board would get this right out of the blue.