This either means that the username and password information in your wp-config.php file is incorrect or that contact with the database server at sql201.byetcluster.com could not be established. This could mean your host’s database server is down.
Are you sure you have the correct username and password?
Are you sure you have typed the correct hostname?
Are you sure the database server is running?
If you are unsure what these terms mean you should probably contact your host.
Forums.
We highly discourage the use of backup plugins here, as they use a lot of resources and can lead to suspension.
Additionally, they generate files that are over our maximum size, so depending on the plugin you use, it may be near impossible to actually use that backup.
In addition to what Greenreader9 said about backup plugins, please see the following article about database connection errors. It specifically lists the error message you are seeing: