Are you doing something to ensure that the minipages are at the top of the physical page? The only two ways I know off-hand to do that are to manually break the page immediately before them or to put them in a float. From your message, it does not sound as though you are breaking the page.
One kludge that should work (and involves no extra packages) is to insert custom spacing. Position the cursor immediately preceding (and just outside) the first minipage, click Insert > Formatting > Vertical Space..., set the spacing to Custom, and insert a negative value (using your preferred units). If the minipages are in a float, this goes inside the float. Paul
