Hi there!
WP Offload SES Support Team here, Thanks for reaching out with your query we would be happy to assist
If you’re receiving the emails from the site and things don’t seem to be stuck in a queue, you can just disable the “Cron not running” notifications.
You can do that by adding the following filter to your theme’s functions.php or in a custom plugin:
add_filter( 'wposes_send_cron_error_email', '__return_false' );
This issue usually arises from multisites. If you have a multisite, it could explain the notification.
If you don’t have a multisite and everything seems to be running correctly, then there might be a problem with the cron check that Offload SES is running. You can check your PHP error logs for anything relevant to this. Otherwise, you can just disable the Cron not running notifications.