A family of Microsoft word processing software products for creating web, email, and print documents.
This is a drawback of using Word calculation fields. Unlike Excel, they do not automatically update when the source data changes. Using File>Print to preview the document will update the calculations (you don't actually have to print, just previewing will work). You can also use a VBA macro to update them:
Sub UpdateCalcs()
ActiveDocument.Fields.Update
End Sub
After creating the macro, you can invoke it with a keyboard shortcut. The only way I know of to make the process automatic is to create a continuously running macro with a timer that fires the update command every few seconds. That takes a lot of processor cycles to run.
You might want to include a portion of an Excel workbook in your Word document to take care of this, that will update automatically when data changes.