If in a group there are more then 6 users (by default) then emails are send using cron. You can set cron interval in settings page of the plugin. Please remember, you need visitor in your website to run wordpress cron.
Is normal cron working in your website?
Please go to Front End PM PRO > Settings > Emails > Email Sending Interval and change the value and save changes. Then wait that much time and see if it start sending emails. Please remember it sends 50 emails per interval by default.