That version is no longer supported ( Umbraco 7 End-of-Life (EOL) ) however, a few things you can do to narrow this down:
Look in /App_Data/Logs for entries around the scheduled publish/unpublish times. You should see messages like INFO - [ScheduledPublishing] Waiting for tasks to complete. If these don’t appear, the scheduler isn’t running or it would provide some form of error/issues its having.
Umbraco relies on hitting its own URL (/umbraco/RestServices/ScheduledPublish/Index) to trigger publishing. If your server blocks local requests, or if the site can’t reach itself (common in Azure or load-balanced setups), the scheduler won’t fire.