Under the menu 'I want to...' select 'View an Item's JSON'
Click on the Map Viewer map that doesn't have the refresh interval options
Scroll down to your Data area
Click on the Pencil (Edit JSON option). You may get a warning the first time about undesirable results ... I would recommend you make a copy of your map first so that you do not accidently break something
Add in the following line (quotes and all) to the JSON for each layer that you want to have refresh "refreshInterval": 1, (Note: I placed mine above the line that has "layerDefinition": and the number 1 is 1 minute)JSON edit
Click the 'Save' button if when hovering over it, it tells you that your JSON is correct.