From what you’ve told us, your single-case-study.php should be the correct file. To help troubleshoot, add this line to your header.php:
<!-- <?php global $template; print_r($template); ?> -->
Then view the source of a single case study and see which template WP is outputting. Once you have identified the file, if the solution isn’t clear, you can post an update here for more help.
It’s possible you may be cached – may need to clear both your browser cache and your server cache, depending on what plugins or host you’re using.