While developing this Add-on to extend the Render Border functionality, I noticed that Blender checks the render border attributes (min x, max x, min y, max y) only once per render execution. By the help of the linked Add-on, animating the values is working fine in the Viewport and also when rendering a single frame (http://i.stack.imgur.com/tCoxp.gif), but unfortunately this isn't working for rendering animations at the moment. It seems that blender is using the current viewport render border attributes for each frame, although the render border scene attributes are driven correctly by the add-on values:
I have no idea about how difficult this is to implement, but what about updating render border attributes for every frame while rendering animations? Or allowing to animate the render border attibutes in the outliner at least? If this is an easy task, it could rapidly improve render workflows and finally speed up the rendering process.
For Add-ons we can use python handlers to overwrite the scene attributes (of course), but wouldn't it be nice (also for upcoming projects) to check this attributes by default for every frame?