In rare instances an email client sends an HTML email without a plain text version. A rough conversion to plain text is performed for incoming HTML-only emails. The Emails related list will contain a copy of the original message, including a link to the original HTML version, which users can refer to. If you don't have that related list, use the page layout editor to add it. If you do not see a link to the HTML version, verify that "Enable HTML Email" is selected (checked) under Setup > Customize > Cases > Email-to-Case
It may appear that a text body does exist when viewing an individual Email Message record because Salesforce also displays a rough conversion. This can be confirmed by inspecting the record's data using Data Loader or a similar tool.