Yes you can recover permanently deleted emails even after deleting them from your trash folder all you have to do is open you gmail then click the drop down arrow from your search box at the top of the screen. it will then ask you several question such as to: or from: subject, has words or date with in. don't answer any of these question just click on the blue search button on the bottom left of the search box and all of your deleted emails will be revealed.
If the deleted emails are less than 30 days old, Gmail trash will keep it otherwise it will cleaned by Gmail. However, if the emails are missing as a result of unauthorized access, you can request Gmail to investigate whether recovery is possible. You can check the below mentioned link for more details: