Not reviving emails from Microsoft Outlook

The company I work for sends emails from Microsoft outlook to various email address including cox emails. When sending emails to the cox emails our clients are not reviving the emails and there is no bounce back on the emails not being delivered. We have tried sending emails to our own personal cox emails to test whether it is on Microsofts part but our personal emails through cox are having no issue. Even replying to a received email from a cox account is not being received on the cox end. These emails are very important and time sensitive. How can we ensure that when we send emails from Microsoft outlook to cox emails that they will be delivered.