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This is an issue with your hosting provider. Email Users make use of the WordPress’ wp_mail() API function which in turns utilizes your web server’s PHP to email interface.

If your hosting provider imposes some limits on outgoing email, you may be able to set up Email Users to honor them. For example, if your hosting provider limits the number of addresses which can appear in the BCC field, there is a setting in Email Users to limit the BCC field to a specific number of addresses.

If your hosting provider limits the number of outgoing email messages per hour or day, then you’ll have to manually schedule your messages as Email Users does not provide any sort of queuing mechanism to schedule mail.

You may also want to look into an SMTP plugin which would allow you to configure WordPress to overload wp_mail() with valid SMTP credentials for outgoing mail. Doing this is fairly common for many hosting providers and Email Users works well with a number of the SMTP plugins.

I have no idea why your hosting provider advised you to use a CAPTCHA solution, that doesn’t make any sense at all.