Keep getting deferred emails

Hello everyone..... hoping someone can help us. We tried doing a mass email on Cyber Monday to all of our customers and for the last week we can't get emails to go out. We keep getting either a "temporarily deferred due to user complaints" or "Domain domain.com has exceeded the max defers and failures per hour (5/5 (100%)) allowed. Message discarded." We can receive all the emails that come in, but can not send anything out. Can someone please shed some light on where to look to stop this? We use ZenCart for manage our store. All help is greatly and genuinely appreciated!!!