Social media links not appearing after "Publishing"

Under "Customizing ==> Menus ==> Social Media Links," I have ticked the "Header Social Media" box. In live preview, the social media links I have set up appear on the Live Preview, just where I want them, and remain there after Publishing. But when I test the page by visiting it (say, on a new browser tab or a completely different web browser), the social media links do not appear. Am I doing something wrong?