I am not sure why this might be happening. When you place your Word file in InDesign, are you going through the Import menu and its options? Checking this box will bring up a rich menu of options and control for Word import when the file is selected:
And at the top of that menu are these options:
The only thing I can think of is that you've imported the document with the footnotes as static text, which is exactly what it sounds like: the notes are no longer linked elements, but just formatted text on each page and at the end.
Import without this box checked, and your footnotes (and end notes, if any) will be imported as live elements.