You can choose where to apply the specific border to within the page border options window.

In the pop up window when you add a page border, go to the bottom right hand corner and it should have "Apply to:" with a drop down.

You should then be able to select "This Section". It will then apply your desired border to the page. You may already have the border style saved and ready to select if you are using different borders for each page. However, if not you may need to recreate the border each time.