I don't think that's related. But first let me ask is this when the user changes a password, or resets a password? If a logged in user changes their password, there is no email sent for that action. However, if a user forgets their password, they have the opportunity to reset it by entering their username and email address. A new random password is sent via email in that case and then the user can log in to change it.
If an email is not being sent, you do need to do some troubleshooting. The plugin uses the native WP function wp_mail for all of the emails that it sends. So, the first thing to check would be to find out if it is sending emails at all, and specifically from WP itself.
To check that wp_mail is functioning properly, create a new user in WP via the Users admin panel. When you do this, make sure (1) you use an email address that you have access to, and (2) check the box that says "Send this password to the new user by email." If you do not receive an email via that process, wp_mail is not functioning in which case it is not the plugin and you'll need to do some deeper troubleshooting as this is beyond the plugin.
If you do receive that message, then I would check to see if the plugin is sending other messages. First I would ask, have any changes been made to the plugin code customization-wise? The process of resetting a password uses wpmem_reset_password() in wp-members-core.php. That function uses wpmem_inc_regemail() in wp-members-email.php. If any changes were made to either of those two functions (or files), you could have introduced a bug. If not, and WP is sending emails, then we need to test to see if the plugin is sending other emails.
In the plugin admin panel, check the box "Notify admin." Then create a new user via the plugin in the frontend of the site. Did you receive messages from that process (one for the new user and one for the admin)?
If none of these are being sent, we need to look into why. Are you using another plugin that has anything to email that could cause a conflict?
If those are being sent, then it seems odd that this one particular email is not. Have you checked your junk mail folder? Also, you might wait a period of time just to make sure that it is not being delayed for some reason, either by your server or your mail server.
Hopefully, that gives you something to go on. Let me know if you track down the issue.