database (MySQL) connection seems to getting closed before session cleanup

In production usage with heavy traffic (many imports) we receive often the below listed error.
My assumption is, that connection to database / mysql is closed before session cleanup is called. On reopening the connection for session cleanup this error occurs then.
Perhaps session cleanup also tries to force a new connection, why ever.

This should be evaluated and changed therefore.

Error on customers server:
PHP Fatal error: Uncaught exception 'PDOException' with message 'SQLSTATE[HY000] [1040] Too many connections' in /usr/share/php/Zend/Db/Adapter/Pdo/Abstract.php:129
Stack trace:
#0 /usr/share/php/Zend/Db/Adapter/Pdo/Abstract.php(129): PDO->__construct('mysql:host=loca...', '', '', Array)
#1 /usr/share/php/Zend/Db/Adapter/Pdo/Mysql.php(111): Zend_Db_Adapter_Pdo_Abstract->_connect()
#2 /usr/share/php/Zend/Db/Adapter/Abstract.php(460): Zend_Db_Adapter_Pdo_Mysql->_connect()
#3 /usr/share/php/Zend/Db/Adapter/Pdo/Abstract.php(238): Zend_Db_Adapter_Abstract->query('DELETE FROM `se...', Array)
#4 /usr/share/php/Zend/Db/Adapter/Abstract.php(664): Zend_Db_Adapter_Pdo_Abstract->query('DELETE FROM `se...')
#5 /usr/share/php/Zend/Db/Table/Abstract.php(1203): Zend_Db_Adapter_Abstract->delete('session', 'modified < 1445...')
#6 /var/www/html/portal-3.0.90/library/ZfExtended/Resource/Session.php(108): Zend_Db_Table_Abstract->delete('modified < 1445...')
#7 /var/www/html/portal-3.0.90/library/ZfExtended/Resource/Session.php(70): ZfExt in /usr/share/php/Zend/Db/Adapter/Pdo/Abstract.php on line 144, referer: http://terminator/portal_d/public/editor