Sending an email once a month helps to create your presence in someone’s mind. Twice or thrice a month develops a connect and doesn’t create a nuisance. But, when you send emails four times a month it creates consistency.
When you send offer emails you can send two emails and then send the third one as a final reminder. But, sending more than three emails just to mention the offer creates a nuisance ultimately losing a subscriber as he/she might mark you as spam. Here, in desperation to get a sale, you’ve lost an opportunity.