Is this header row formatted with the "Repeat as header row at the top of
each page" attribute? Or is it a header row purely by virtue of the logic of
the table?
What version of Word is this?
If the header row is not explicitly formatted as "Repeat as header row...",
then choosing that option should solve the problem. Method: select the first
row of the table, right-click and choose Table Properties - Row tab, and
click the Repeat... option. You then should remove any manually inserted
copies of that row, as Word will handle the repetition as needed.
Or... have you already done this, and the repeat is occurring in the wrong
place?