That's interesting ... Are the backups working for you, or does the error stop them from running? So it solved it in the older version of WordPress but not the newer - that's so crazy! And you're up to the 3.4.5 plugin version on all sites still affected?
The error itself actually means the plugin can't find the MySQL on your server :( We have a constant you can define in the wp-config.php file that will tell the plugin where to find that, though ...
I wonder if you'd be willing to contact us via the support tab on your site's BackUpWordPress page? We might be able to help you find the right path to use to get that variable assigned correctly if you need help with that.
Kat