Eliminate Pingdom Alerts for Several WP Sites on Dedicated Server

We are getting constant brief Pingdom Alerts that several of our sites are down on a dedicated server. They are mostly WP sites. They do load quickly (under a minute) and most have minimal content and plugins. Our managed host support has made a lot of upgrades and tweaks but has been unable to resolve the alerts issue on several of the sites. They indicated that it could be a high volume of "JOIN" queries causing the issue, but unfortunately the MySQLTuner script they use doesn't identify specifically which sites/scripts are using the queries improperly. However, since they happen pretty consistently, they recommend to narrow it down by viewing the MySQL processes as they take place. They suggested an easy way to do that is to SSH into the server and then watch 'mysqladmin proc' I need someone experienced to do this and use any other monitoring tools to provide us a report on what exactly is causing the problem and their recommendations to resolve it. This project is just for the report and the coder is not required to make the actual changes on all the sites other than to test their recommendation on a single site.