Ensure that the email is set up and configured in Jira itself and that the standard notifications for Jira Service Management are being sent successfully. 

This Atlassian troubleshooting guide is useful to resolve these issue: Troubleshoot email notifications in Jira Service Management.

If email is working with the exception of the ones for comment added or edited notifications, review the Configuration pages and in particular ensure that the Enabled for project option is enabled.