Emails erroneously marked for deletion, not delivered

About 90% of the incoming messages on one of my @cox.com email accounts are not delivered to my Outlook 2016 email client on Windows or Mail.app on macOS.  When I look at the webmail page they're there, but displayed in strikeout type.  A few are not in strikeout, and those are delivered properly to the client. This doesn't happen on any of the other accounts.

When I called Cox support it sounded like the tech quickly referred to a script: "The email system is having problems." (Yes, I know, because it took them about 18 months to migrate one of my accounts from the "old platform" to the"new platform.")  He then explained that messages in strikeout are "marked for deletion."  Of course I didn't do so, and asked if I could un-mark them.  "No" was the answer.  

"So I have to just sit and spin until you get this fixed?" I asked.  His reply: "I might not have put it that way, but since you did, yes."  I won't be holding my breath for a fix, but I will be moving subscriptions on that email ID to other @cox.com email accounts.  And looking for a new email provider like Proton or Zoho.  Cox says email is a free service and once again proves that you get what you pay for.