Please take a look at the official documentation:
As you might notice, there are specific conditions that have to be met in order for the Play Store to auto-update apps.
Depending on how you charge and use your phone those conditions might not be met for prolonged periods of time.
From my personal experience, I sometimes fall behind on app updates for 2 to 3 days, but rarely for more than a week. Your milage might vary.
Also, for an app to be seamlessly updatable, it must target a modern API level. Many apps are still targeting low API levels, which means that to update them you must click "install" button every time.