How to stop an iPhone from automatically deleting trashed emails over a week old?
To change the setting, go to Settings &rarr; Mail, Contacts, Calendars &rarr; iCloud &rarr; Mail (under Advanced) &rarr; Advanced &rarr; Remove (under Deleted Messages) and set the time period after which deleted messages are removed.

You should not expect anything deleted to persist at all. You have instructed for it to be deleted and this is what you should expect.