Here are the steps to try to retrieve the backup:
In your database manager, run this query:
SET @backup_values = (SELECT option_value FROM `wp_options` WHERE option_name = "buttonizer_rules_backup_6");
UPDATE `wp_options` SET `option_value` = @backup_values WHERE `option_name` = "buttonizer_rules";
( wp_options may be different for you whether or not you had used a different prefix during the WordPress setup )
After running this query, it should copy the backup page rules back into the page rules data.
But since the backup data is still in the old format, we need to make Buttonizer update the page rules data again.
To do that we will turn back the migration version in buttonizer_settings.
There's unfortunately no other way to do this other than manually changing the version.
In wp_options, look for buttonizer_settings.
You check the Show all option then search for buttonizer_settings.
Then in the option_value, find the migration_version and change the
7 next to it into a
After that, you should be done with updating the data.
You can then return to the Buttonizer editor and press
R again just to make sure.