I set vertical scrolling on the Container and it does scroll.
The problem is that as soon as there is enough data to scroll, the first component is clipped. I tried different components in the first position but they always got clipped.

Image1 shows the top of the screen when there is no scrolling.

Image2 shows the same area after more data is added and scrolling kicks in.
The first component has been reduced in height.
As I mentioned I have found a good workaround for this problem, so it is not a big deal. I used to construct the whole form with GridBagLayout, now it is a BoxLayout with GridBagLayout in the boxes.
Thanks,
Martin