Word is hit-and-miss when it comes to applying borders. It works (or has for me) if you specify a border for a heading style (e.g., h1), but others have reported that it doesn't work in some situations like yours. You can submit a bug report at
http://www.madcapsoftware.com/bugs/submit.aspx, but I'm not sure if MadCap can take care of the problem since Word is pretty flaky about rendering stylesheet code from sources outside Word.
As a workaround, you might try not applying the border from within the page layout, but rather apply it to whatever tag you're using for your footer. For instance, if you created a custom tag called p.footer, then set the border properties on that tag instead of using the design options in the page layout. See if Word likes that better.