KB 2975003 confirmed this was a problem! The KB says: "...compose or edit a Calendar item by using Outlook Web App...and then save the item. When you open the item in Microsoft Outlook 2013 or Outlook 2010 in online mode, the body of the item disappears." We scrambled and updated our code to set MAPI codes to fix the problem in our code. But they reported their end users were still having the same problem on NEW items.
Now there is a fix: install Cumulative Update 6 for Exchange Server 2013: 2961810