Mail is being deleted automatically

There are n+1 trashes: one for each account, plus one "On my mac".

The rules are actually pretty simple: when you delete a message, it goes to the respective trash. Messages that you had previously moved to a folder under "On My Mac" and that you subsequently delete, go to the "On my mac" trash. Other messages go to the trash folder corresponding to their respective accounts.

Again: there is no way to tell Mail.app to behave otherwise when you delete a message.

Selecting a particular trash does not mean deleted messages will go there.

Your Trash subfolder for that account will be named the same as your mail name whether it's local or server. On My Mac trash folder belongs to the local mailboxes created outside of the Trash, Sent, or Draft mailboxes.

What I meant was to expand the account name in the sidebar and look for the server trash there.

Have you checked online that the mail are being deleted?

Possibly viewing emails from a particular time period.

Who is the email provider and is this set up on any other devices such as an iPhone?

No problem!

One way to get around automatic deletion of mail is to setup a new account and forward to it from this one your having problems with, sounds like an old account from a service provider.