I saw the upgrade was just an upgrade to phpmailer and went ahead and installed the plugin upgrade.
Where the plugin was definitely working before for 2+ weeks, I have not received emails since (when I should get at least two a day for backup reminders) the upgrade.
Sending the test email through Chrome gives this error:
The website encountered an error while retrieving http://fullfeminine.com/wp-admin/options-general.php?page=amazon-ses-and-dkim-mailer/configure-smtp.php. It may be down for maintenance or configured incorrectly.