Anita,
I make tables all the time and they all display a border at the bottom of the page. Try this to get back to square one:
In the Table Designer CLEAR the Draw Bottom Ruling on Last Sheet Only box, that is UNchecked.
Select the entire table, and select the menu Table > Custom Ruling & Shading.
In the dialog box, CHECK all boxes and select From Table in all lists and dropdowns.
Click Apply.
This makes all the rules and shadings match what the table style dictates. If some cells requires special rules and shadings, then you have to select those cells and use the custom rules and shadings box to set them the way you want.
I am guess that maybe the previous writer gave some rows no rules and that is where the page is breaking, but just a guess.
There should always be a rule at the bottom of the page unless you check Draw Bottom Ruling on Last Sheet Only in the table designer OR add custom borders of none at the row where the page breaks.
Good luck,
Van