My dedicated server keeps getting very slow that it fails to load the application

SQL Server Express does go into an idle state, so I believe, when it's not being used: http://blogs.msdn.com/b/sqlexpress/archive/2008/02/22/sql-express-behaviors-idle-time-resources-usage-auto-close-and-user-instances.aspx

(Sorry, I didn't look at the date.... sometimes SF shows really old posts).

I am not an DB expert, but it looks like invalid use of Advisory Locks somewhere in your application.

PostgreSQL provides a means for creating locks that have application-defined meanings. These are called advisory locks, because the system does not enforce their use — it is up to the application to use them correctly.

and

Like all locks in PostgreSQL, a complete list of advisory locks currently held by any session can be found in the pg_locks system view.

Edit:

Looking into moodle source code, /moodle/lib/dml/pgsql_native_moodle_database.php I just found something, that might be interesting:

public function get_session_lock($rowid) {
    // NOTE: there is a potential locking problem for database running
    // multiple instances of moodle, we could try to use
    // pg_advisory_lock(int, int), luckily there is not a big chance
    // that they would collide
    if (!$this->session_lock_supported()) {
        return;
    }

    parent::get_session_lock($rowid);
    $sql = "SELECT pg_advisory_lock($rowid)";
    ...
}