Sounds like there is a layout object at or near the border of your layout part. You will not be able to drag the border up past it. Also, if this is FIleMaker 12 and not a classic themed layout, you must drag from the left of the right hand layout border.
On windows, if you want to drag the border up past a layout object so that it now becomes part of the layout part located below the border, hold down the alt key while dragging the border.
Yes, I realized that the background color was an object in and of itself so once I reduced its size, I was immediately able to drag the bottom border!