Mail in inbox after a certain date is deleted. How to control that?

The setting sat comer is referring to is for deleted emails, not those in the Inbox.

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Is this issue for all of your email accounts or one particular one? If the latter, which one?

Your email provider may also control how long emails can reside in the Inbox, and many offer settings for you to adjust.

Do you know if this account is a POP3 or IMAP account?

There is no function in Mail to automatically delete messages from the inbox.

Open Mail and go to it's Settings and click the 'MailBox Behaviors' tab and select when they are deleted!

Who is your email provider?

Ok, thanks. In this case you will need to contact them directly to see if there are any options that they provide you to manage your email account/mailboxes.