No, suppression doesn't have anything to do with it. I would take a look at the "Keep Together" settings for the Group and the Sections. I suspect that you have "Keep Together" turned on for the group which will force a new page if there's not enough room for the group to print at the end of the current page.
However, turning this off may have the side effect of showing just the first section of the group on one page and the rest on another. In some situations, this is an issue, in others it's not. You'll have to take a look at how it's working for you and decide how you want to handle it.
-Dell