You have to be very careful about who you email and how often you email them. If your emailing offers to your mailing list every day then it's pretty obvious that they are going to get annoyed and block you.
I do a monthly newsletter at work but to be honest, the amount of opens we get are pretty low. I keep the newsletter consistent from month to month just to keep the company's brand a push just to help people remember us. The only problem is that some people don't want to hear from us although they have signed up to our newsletter mailing list. This doesn't have any consequences, just feels like a bit of a waste of time sometimes.