There are couple of directions that may cause missing emails:
- Do you use also PC / Web clients for your account? If so, is it possible they are configured to POP3, and hence "pull" and delete the mail from the server (as POP3 often does). If this is the case, you just need to configure your PC client to "leave messages on the server", or even better, switch to IMAP. Also look at your account settings on that issue.
- Please check if you do not have rules that somehow move the mails to other folders. You can search on your stock client to find one of those missing mails, and if it is not in inbox, look in BlueMail in that same folder.