You see records for each outbound message in the Emails related list on the case, however some recipients are not receiving the messages from Email to Case Premium.

Have the message recipient check the Junk, Spam, or other folders of their email application. If messages are located, add a Sender Policy Framework (SPF) record for Salesforce to your organization’s Domain Name Server. Email messages have a higher chance of delivery to the inbox when validated using SPF.

For more information on how to configure SPF, please refer to the following articles:

• Sender Policy Framework (SPF) and Salesforce SPF records
• Improving Outbound Mail Delivery in Salesforce