The first thing that comes to mind is the flatness of the routing surface. If the ends of the table are higher then the middle it might be more then a feather board can deal with.
Take a 4 foot level or something that is able to span the top and is straight then with a light behind see where the light show through or take a business card see how that slides under in the middle. To be sure turn the level over and see what it looks like. If you have a space in the middle your top is not flat and the board will span the area giving you a case as you described.
If this doesn't seem to be the case then at least this thought can be eliminated.