That sounds like the issue… something is causing some kind of error during the sending of the email (although the email is actually getting sent), and so the wp_mail function is returning a false value. Note that plugins, like Postman, are simply replacing the pluggable wp_mail function to send emails via SMTP instead of PHP sendmail, so my own plugin is not aware of how the email is actually being sent. My plugin just formats the email data and then calls the wp_mail function to actually send the email. My plugin does NOT have a retry function, so it will not try to send an email again immediately when a FALSE value is returned from wp_mail (so most notifications, such as sign-ups and clear emails will NOT be sent multiple times). However, if a true/positive value is NOT returned from wp_mail when it is sending reminders, then those reminders never get marked as being sent and will be resent again the next time the CRON job runs.
Not much I could do about that in my plugin unless I change my code to always mark reminders as being sent, even when wp_mail returns a false value. But, that would be like treating the symptom of a problem instead of fixing the problem.
So, for now, I’ll mark this as resolved since my plugin is working as designed, and you should contact the developer for Postman (which I also use, btw) to see if they can help you track down the issue with your email/server configuration.