>>> mysql_connect():
Looks like this message is coming direct from the server on which the forum database resides. As eric has correctly pointed out, the limit of maximum concurrent users has been reached.
The server will have a maximum number of users that can connect to avoid ddos attempts. This limit is often set by the hosting company who generally configure all the mysql & php security settings for the server. They may need to contact their webhost to get the limit increased/upgrade hosting package.