Error establishing a database connection! Please HELP

Sometimes when I click on the “Publish” button to post a new article on my WordPress blog, then this error message appears:

“”Error establishing a database connection… This either means that the username and password information in your wp-config.php file is incorrect or we can’t contact the database server at localhost. This could mean your host’s database server is down…..””

Despite the error message appears, my post got published and there is no problem with visiting my site. This error does not come after each post publication. Sometimes it occurs. (My hosting reseller provider changed my server some days ago and this problem began after coming to the new server) What is the problem and how to solve it, please tell …… Thanks.