I am not sure if this is your problem but as nobody else has answered (since July!):
There are two types of render border. The view-port render border and the Camera render border, they are independent.
You can select a border for view-port render in any viewing angle and in render preview mode it will show that portion of the view rendered.
But if you hit F12 the render will be always be from your active camera’s view and will not take that border into account.
To select a border for the camera view you have to select the border in the camera view.
Ie: go to view menu, select cameras-active camera (Numpad 0) and then set your border from that view.
When you hit F12 you render from the camera view and the border that you set in the camera view is the one that renders. Not the border you selected in any other view-port angles.
If you do both (select one border for the camera view and another in any other viewing angle), you have 2 independent borders one for the view-port and another for the camera. To deactivate them you will have to deactivate them separately.
Hope all that makes sense and is useful for you.
If that is not your problem I can not help, border render works as expected for me.