The full T&C actually says you can earn 10 entries for receiving e-mails, essentially 2 extra entries for saying yes to their mailing list (or not “no”, oddly) 5 separate times. You know a lawyer got paid well to write this:
Opt-In to receive AAdvantage eShoppingsm Marketing Communications: After you register, you may be asked to sign-up to receive email marketing communications. If you agree to receive these communications and/or if you do not “unsubscribe” from email communications if you are already receiving them, you will receive two (2) additional entries into the Sweepstakes, so long as you remain opted in as of the end date of the Promotion Period. Limit: You will only receive ten (10) entries during the Promotion Period for opting-in to email communications.
In other words, we want to reward you for not unsubscribing.
You also earn extra entries for purchases on the shopping portal.
Anyway, you can enter every day between now and the end of September.