Q: Disappearing email on my Mac & Devices

On the computer.

Try rebuilding the mailbox.

Rebuild mailbox

If that doesn't work, try re-indexing the mailboxes. This can take awhile if you have a lot of mail.

Reindex messages        For El Capitan, try looking in V3.

Reindex messages (2)        See post by Linc Davis

Please do the settings as in screen you might have missed some of them .

Please post for further assistance .

Thanks !