The above errors are indicative of a hosting/platform problem, not really MODx, the problem I see with this :-
I think the Core scripts should stop running if the MySQL Database failed to respond the connection.
is that how do you decide to start processing again? If you stop processing you won't make any more connections, so you won't know when the DB is working again.
Admittedly dumping the error message is not always desirable, this thread
http://modxcms.com/forums/index.php/topic,33898.msg207757.html shows how you can override this behaviour if you wish