It's so frustrating. I KNEW how to do it (select the rows and click "keep with next") but it doesn't work anymore.
How do I keep all the lines on the same page, causing the table to move to the next page if there's no space left on the current one?
It's on the Paragraph toolbar (which is generally on the "Home" tab of the ribbon). Click the tiny arrow in a square on the bottom right hand corner. Choose Line and Page breaks and tick the 'keep with next' box.