I too had a problem with Google Apps Gmail and “Email could not be sent”.
My website is hosted on it’s own domain and Google Apps MX records are configured in DNS. Google Apps Toolbox Check MX reports everything is fine: https://toolbox.googleapps.com/apps/checkmx/
My hosting provider (WPEngine.com) does not offer e-mail services, which if it did can cause other well documented problems because mail will be sent to the hosting provider’s local mail servers instead of gmail for the domain. See the Google Apps Forums for more info.
Two-Step Verification is enabled via the Gmail Security settings (Gmail Account -> Security -> 2-step verification).
Configured Easy WP SMTP as so:
From Email Address: [email protected] <– alias setup in Gmail
From Name: WordPress
SMTP Host: smtp.gmail.com
Type of Encryption: SSL
SMTP Port: 465
SMTP Authentication: Yes
Username: [email protected] <– real user in Gmail
Password: < password used for https://mail.google.com >
Enable SMTP Debug: Checked
Sending test e-mails via the “Test & Debug Settings” section of the plugin failed.
I found the problem in the “SMTP Debug:” output panel. The Google Mail server said “Application specific password required” or something very similar.
Woo Hoo!
I logged into the Gmail admin@mydomain account via my web browser, navigated back to the Gmail Account -> Security -> 2-step verification and created a new application password for “WordPress”. Pasted the application specific password into the plugin:
Username: [email protected] <– real user in Gmail
Password: <application specific password for WordPress>
and e-mail works fine! Sent various test e-mails to Google Apps mail, regular gmail and external domain accounts. No problems!
I now receive WordPress comment notifications!