Re. your comment. That shouldn't happen. Is the version of Times New Roman that you are using a Postscript font? You might be using an old TrueType font that came with Word, or a newer TrueType font that is rendered as an Open Type font. Make sure you only have ONE version (preferably an Open Type version) of Times New Roman open and active on your machine and try the conversion again. If you can't manage that, or it still doesn't work correctly, try another oldstyle typeface such as Baskerville Old Face, Garamond, or Goudy--all three of those come with Word, so you should have them. That said, Word is not a page layout program, and it sometimes renders PDFs erratically. (I've had to use Word from time to time to layout a book, and I've found lines slipping from one page to the next, or sometimes a line at the top or bottom of a page goes missing.) So be sure to check your results carefully.
Is this the sort of issue that might show up if you downloaded my conversion tool and were using a different font? A PDF conversion program is an extremely powerful tool, but you're only using it to do one task at a time: Converting your PDF document into print-ready Word PDF format. A font conversion tool is specifically designed to be used to create PDF files that will look like the Word file that you are using, because that is the only thing that it can convert--it can't work with or make changes to the original document. Most font conversion programs can be used to read a PDF and convert it to another font, or it can give you suggestions for changing your print-ready Word document. If you do have a problem reading your own PDF file, you can use the Convert Your PDF page to PDF feature to.