Outlook Emails Going Crazy on Mac and PC's

In the last few weeks we've had a multitude of problems with our Cox emails, disappearing, being delivered to only one or two of our four computer devices, showing up only in the webmail, etc. We pay extra for tech support. I've been online with three Cox tech people. It just got worse. Had a Cox tech man out here for 31/2 hours. Didn't accomplish anything. We've found a lot of words online about Outlook causing similar problems for years. Maybe it's not a Cox-caused problem but surely there must be a tech "specialist" who's heard of this and knows what to do.