Your problem might be that when you try to drag the table borders they go in little jumps, and though these are little, they may be just too much! If this is, in fact, the problem, press Alt while you drag and you will find that you can move them as much or little as you like.
Also, if you try to move a border to a part of the page (the bottom) which is below the margin setting then it will go to another page. You need to move the bottom margin right down as low as seems reasonable before dragging the table border. Do you know how to do that?