There is a setting on the Support Settings page in Salesforce that dictates if the Case Owner receives an email notification when a new comment is added to a case.
To ensure the Case Owners receives an email notification when a new comment is added, navigate to Your Name > Setup > Customize > Cases > Support Settings.
On the Support Settings page, Click the Edit button.
Under Use this setting to notify case owner when a comment is added to a case, check the box next to Notify Case Owner of New Case Comments.
Navigate to the Setup Wizard for E2CP. On the Inbound Configuration page, choose the Trigger User Emails option.
Troubleshooting Tip: An email notification will not be sent if the Case Owner is the same user as the Context User for the Email Service’s routing address. Salesforce recognizes that the case owner created the comment, and therefore would not need an email notification. Salesforce is unable to distinguish an automation action performed by a user from a manual action. We recommend you assign a dedicated API user as the Context User or select a user who will never own a case.
Troubleshooting Tip: Login to Salesforce as the context user specified in your routing address. Add a comment to the case in question using the standard Salesforce new comment page. If an email is sent to the Case Owner, contact Internet Creations for troubleshooting assistance. If an email is not sent, contact your Salesforce administrator, consult Salesforce Help & Training, or open a case with Salesforce support.
Verify the case owner's email address is valid, particularly in sandbox environments where email addresses are often appended with .sandbox name making emails undeliverable.