Hi MAT16A
welcome to the Apple (user-to-user) Community!
Re: "Mail : Where have my seen emails disappeared to? : Why are they disappearing from my In Box anyway!"
Apologies for the tardy reply. As your Mac OS is an earlier version, it is not easy to give step-by-step help.
Seems you would need to go into Mail > Preferences > to check the settings that are in place,
and to make any necessary changes that suit your way of working.
The articles below are the earliest I can find: they are for MacOS 10.14 (Mojave) but may give some help / idea.
Eg: check if a filter is set that moves the messages automatically, and see if you can change that.
If settings say only "unread" messages are to remain in the inbox, then the read messages may be moved
Read emails in Mail on Mac - Apple Support
says:
"In the Mail app
on your Mac, do any of the following:
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Re: "Why are they disappearing from my In Box anyway!"
If you want to keep the current settings yet keep certain read messages in the inbox, you could manually mark them unread.
Eg: Mark emails as read or unread in Mail on Mac - Apple Support
says:
"Email messages you haven’t read yet have a blue dot or star (for messages from VIPs) next to them.
When you select a message to read it, the dot or star disappears.
If you want, you can manually mark messages as read or unread.
- "In the Mail app
on your Mac, select one or more read or unread messages. - Choose Message > Mark > As Unread or Message > Mark > As Read to change the status.
- To mark one message, you can also swipe right with two fingers on the trackpad,
then click Mark as Unread or Mark as Read".
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Re: Where have my seen emails disappeared to?
Check the "Archive" mailbox / folder to see if read eMails are moved there. Check for a "Pending" Mailbox.
or
See if there is a rule in place that determines where read messages go:
- In the Mail app
on your Mac, choose Mail > Preferences, then click Rules. - To review an example of a rule, select a provided rule, then click Edit. To close the rule, click Cancel.
How to: Use rules to manage emails you receive in Mail on Mac - Apple Support
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Else:
If messages are in a "Recovered Messages" mailbox in Mail on Mac
If an email account in the Mail app
on your Mac has a Recovered Messages mailboxin the Mail sidebar, try these suggestions.
- If Mail moved messages to the Recovered Messages mailbox when it updated your email library after a macOS upgrade, drag the messages into another mailbox.
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More info.
There is an Apple Mail Support website (info. / support / contact):
Mail - Official Apple Support
All the best :-)