Related Questions:
Why can't I find old emails?
Where did my guests' email history go?
How far out can I Schedule an Email?
Answer:
Regardless of which email provider you integrate with, emails are stored in Event Temple for two years. After this, they will be permanently removed from the system.
This includes sent/received items as well as any scheduled emails.
Please note, this does not affect email communication in your email provider. Eg. if you use Gmail, the emails will still be available directly in your Gmail account.