I have tried going to File | Save As | Reduced Size PDF, but each time I do so, I get a warning that "The PDF document contained image masks that were not downsampled" and the resulting file is the same size as the original file. The same occurs when I try to reduce the PDF through File | Save As | Optimized PDF.
How can I reduce the size of the PDF?
The Reduced Size PDF assumes certain parameters in terms of degrading image quality and eliminating extraneous metadata and non-essential aspects of a PDF file. Assuming that the PDF file already meets these criteria, the Reduced Size PDF option won't do anything more for you.
Another save option, Optimized PDF, allows you to set parameters by which you can further possibly reduce file size including the type of file compression and quality setting and the resolution to which you downsample the images. Note that for the most part, these options can significantly reduce the visual quality of the resultant PDF file yielding fuzzy-wuzzy and/or pixelated raster images.
Note that you cannot legislate the size of an existing PDF file. At a certain point, you sacrifice quality or even content in its entirety. Note that for a PDF file that has no raster images, just text and/or vector graphics, there is usually not much you can do to significantly reduce the size of a PDF file other than going back to the original source document and deleting content!