There are a couple of directions that may help with finding missing emails:
- Do you use other clients or devices with an affected account? Is it configured as a POP3 protocol?
This setup can "pull" and delete the mail from the server (as POP3 often does). If this is the case, you just need to configure your other client to "leave messages on the server", or better, switch to IMAP. - Check if you have rules or spam filter settings on your provider client that move the emails to other folders. Search in Trash / Junk / Spam / Other folders.
- Use the search feature, in both BlueMail your provider's email client.
- Use your provider's email recovery features if the email was deleted.