Hi folks... here's a brief elaboration.
First, the CSS editing features give you a choice whether to "add" your CSS to the existing CSS or to substitute your CSS instead of the original. If you choose the latter, you may well first copy the original CSS and use that as the basis for your modification. So copying and pasting the original CSS is not wrong, it just is not the tidiest way to proceed if you just want to make a few mods.
Second, the reason that the banner is "lost" is that the original CSS specifies where to fetch the image from using a path that is relative to the original CSS file location. With the editing option, the CSS file is going to be in a different directory, and thus fails to refer to the correct path for the image. So to overcome that, just upload an image and then use the path to that image in the CSS.
So, next, you need to know how to upload an image: Dashboard > Media > Add New is one way.
That done, you need to know the path to that image, which is not necessarily obvious. One way is to go to the list of media items (Media > Library), and for the image of interest, and then select the View link. (You have to hover the mouse near the item to get the View link to appear). That will show a page with just the one image in place, and you can view the source or look in the browser status bar to see the path. It will be something like:
http://yoursite.files.wordpress.com/2009/01/imagename.jpg ... where 2009/01 is the month you uploaded it.
Now, how to put this into your CSS? Essentially you want to duplicate the CSS that was originally showing the image, and substitute in your new path.
If you are using the Add CSS option, then:
background:url('http://yoursite.files.wordpress.com/2009/01/imagename.jpg') no-repeat left top;
(If you are using the replace CSS option, then edit only the background attribute.)
Hope that helps.