This applies to both Standard and Deluxe Public Sites.
When a secondary page gets published on the public site, it doesn't automatically get added to the site navigation the way that a primary page would. You have to add the newly published pages to the navigation using the Menus Editor:
First, find the Menus Editor under Appearance > Menus in the WordPress Dashboard
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Then, select which pages to add to your navigation and Add to Menu.
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The pages will be added to the bottom of your navigation list. Drag and drop them to the correct position
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Finally, always remember to click the Save Menu button in the bottom right corner of the page and look for a confirmation message
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Your secondary pages will appear under your primary navigation.