If these were Archive Mail in “Local Folders” under your mail account, then sounds like either the archive folder mail has either eg: been moved to somewhere else in your mail account or other mail account if you have more than one account, or something has happened to your existing mail database.
So I would first “do a search via the search field” and choose custom folders and select all your mail account folders. Then search for “a word or words” in one of those archive messages by the eg: subject or message body to see if they appear in any other non archive mail account folder/s.
If the archive messages then don’t appear in any other mail folder, then suggest next, if you have to making regular eM Client backups either automatically via Settings or manually via the Menu, to try restoring a dated backup when you know the archive folder was there via “Menu / File / Restore”. Any new mail since the restore date will then update when eM Client syncs.
The dated backup.zip files “by default” would be in your “Documents / eM Client” folder.
If you do try restoring a backup make a manual backup of your current database first via “Menu / Backup” incase you need to restore back again.
Also if you have been making copies of your computer hard-disk user profiles or making computer images to other internal or external drives, and you don’t want to restore the entire backup, you can also do a “Partial Restore” either from a eM Client backed up hidden mail database folder or from a eM Client backup.zip file as per my post in the following thread.
Archive folder mail “might also not be showing” if eg: you have V10 and had been making External Archives in a .emdf data file, which then might have been “Unmounted” so then just needs to be Mounted again to show the archive mail.
So if you have V10, go to “Menu / Data Files” and then click "Mount along the top and see if there is a eg: Archive .emdf file or any other named .emdf file there. Data Files when mounted show above Local Folders below your accounts. Also emdf data mail store files are normally located by default in the “Documents / eM Client” folder.