Do you host your own server?
If not then contact your hosting company to see what options you have.

If you have access to the server you can navigate into the folder that you're missing emails from and look for the appropriate GRP file. GRP files contain a full day of email, so you'll want to check for the presence of one with the date in its name that is associated with those missing emails. If those GRP files are not present then they will need to be restored from a backup or from your local client profile unfortunately. Let us know how it goes when you get a chance to check. Have a good one!