Since there are a lot of AJAX requests firing off simultaneously in many places in the manager, there are a lot of requests/connections needed to support the Revolution manager. That said, you are not using persistent connections, so each request is creating a new connection. You may want to try using persistent connections.
In your core/config/config.inc.php file, there is a $driver_options array where you can add options for the PDO driver. To use persistent connections, which will reuse the connections among the same pool of 20 you are allocated, simply set the following driver attribute to true:
$driver_options = array (
PDO::ATTR_PERSISTENT => true
);
I'm assuming the problem is you are also being limited in the total number of connections you can have at once, so reusing the same 20 may help, or it may not.