UPDATE:

There are actually 70+ emails in the database. They all have 0 for the mail queue value. I set one of them to 1 and waited for cron to execute. When cron executed, that value went back to 0 but no email was ever sent out.

Rescuing text of the issue that was lost from our server crash...

"For some instances, Composr does not send out notifications via. Email when it
is supposed to.

Steps to Reproduce:
Whatever method entails an email notification, execute that method and see if an
email is sent out to the account.

Additional Information:
Examples of it not sending out emails include:
*Email verification on website joining
*Some of the notifications which email is set as a means of notification do not
get an email

Composr: 9.0.13
OS: Linux
Host: Webhostinghub
Domain: http://www.wrrj.org
Cron: Set for every 5 minutes
Batch email is enabled in Composr options

Examples of when email does work:
*Reminders of events
*Hack attempts / automatic blocks
*Website errors

I have not tested / confirmed other methods of email notifications, whether they
work or don't work.

I have confirmed the execution of the cron job that is set to execute every 5
minutes. The emails still do not get sent. I'm not sure how to find the mail
queue in the database. If that's needed, perhaps let me know where to find it?
Thanks."

I did spot a small bug, the count of the mail queue in the staff checklist block doesn't change when it should, because CRON isn't decaching that block. That will be fixed.

Otherwise, the mails will be being sent, so it will be something in your email infrastructure rather than Composr. E.g. a spam checker at some point in the SMTP process, or on your machine.

m_queued=0 means the mail has been sent (i.e. is no longer queued, now it is just there as a log). You can view the mail log/queue from /adminzone/?page=admin_emaillog.

(Request for re-opening)

Upon further investigation, I've done some tests with the assistance of webhostinghub. I've found that Composr is trying to send out emails, however they're being blocked by gmail and other email domains on account of them identifying the emails as spam and malicious. Therefore, people are not getting them.

I've also tried SMTP and I get the same results.

Composr will be sending them to the webhost's SMTP server, and then they will be stuck in the webhosts email queue as rejected, or sent out but sent straight to spam. This is not an Composr problem. It may be you have something like SPF on your domain that isn't correctly configured, or some keyword in your sitename (or similar) that triggers spam filters.