Unable to toggle between Manual and Automatic for Download cache when the 'Allow anonymous access to your organization's website' checkbox is unchecked or checked for existing items from the Data tab.
From Organization settings, check the checkbox 'Allow anonymous access to your organization's website' > Save > Add the ArcGIS for Service as an item to ArcGIS Online again > toggling works for download cache in <a href="https://hub.arcgis.com/admin/data" target="_blank">https://hub.arcgis.com/admin/data</a> for this newly added item.