Case Comments not being sent to Case owner

Case Owners will not receive Case Comment notifications when they are leaving Case Comments on Cases they own. Since they are leaving the Comment on the Case, they already know what they entered, so there is no need to notify them via email. 

To check if "Notify Case Owner of New Case Comments" is enabled. Please follow the following steps:

Classic: Setup | Build | Customize | Cases | Support Settings

Lightning: Gear Icon | Setup | Feature Setting | Service | Support Settings

From there, you can see if the "Notify Case Owner of New Case Comments" is enabled. If not and you want to enable it, please follow the following steps:

1. Click "Edit"
2. Tick the checkbox after "Notify Case Owner of New Case Comments"
3. Click "Save"

Note: If the steps provided still does not resolve the issue, you can try these next steps:

1. Setup (gear icon)
2. In quick find, type in Process Automation Settings
3. Scroll to the last part of the page to find "Send an email notification every time a process, workflow rule, or Apex trigger creates or updates the same record that triggered the automation. When this setting is disabled, no email notification is sent when the same record is updated via automated updates."
4. Make sure the checkbox is ticked before clicking Save.
 

Please contact Salesforce support if the issue persists.