I have an email alert sending issue in BPS Pro. The test email function works fine, email sending working both wp mail and php mail functions. I setup the From and To fileds in the configuration, but if is a trigger event, no email sends to my email.
I attached a screenshot about the BPS settings. I use WP Mail SMTP plugin to send emails, these are my smtp settings.
In your screenshot the Send email alerts… From text box is blank. If that is not the problem then check your spam or junk folder to see if the emails are being spammed/junked. Your host server might be rejecting the email alerts as spam since they contain links. Another possibility would be WP Standard Cron jobs are disabled. Are you disabling WP Crons in your wp-config.php file?