This reply does not form an attorney-client relationship between us, nor is it intended as a solicitation.
The answer to your question depends on the service provider, quite honestly. Emails (even when deleted from the account's inbox) can persist on the Internet in various forms. Sent emails will remain on whatever servers they passed through in transit. Some service providers may keep emails (or logs of them) for extended periods of time. You'd need to subpoena those emails from the service provider, if they are available. Odds are that if the provider did not keep them, they are "out there" somewhere. The trick at that point is finding them.