To sign out of Cortana specifically, go to the Cortana menu and open "Notebook", and go into the "About Me" section. You'll see your online account listed there. Click it, then click the same account (otherwise you won't see the option to sign-out!) again inside the popup to get the "remove" option.
Then sign back in to Cortana. Connection problem solved. Cortana will re-connect and refresh your information (which somehow got corrupted).
Note to Microsoft: THIS SIGN OUT OPTION IS IN THE WRONG DAMN PLACE. IT SHOULD FEATURE WITH FAR MORE PROMINENCE. AS IT IS, USERS HAVE VIRTUALLY NO IDEA WHERE THIS HIDDEN OPTION IS.
THE SIGN OUT OPTION SHOULD BE UNDER THE CORTANA BURGER ICON (WHERE HOME AND NOTEBOOK IS), JUST LIKE IT IS FEATURED IN THE START MENU ABOVE SETTINGS AND POWER.
!! VERY POOR DESIGN - USERS CAN'T FIX THEIR PROBLEMS IF THEY CAN'T SEE THE OPTIONS THEY NEED !!