it looks like that the only reliable way for PDF to AI conversion is doable only in case of full PDF files that were previously saved in the original Adobe Illustrator using the 'save for editability' option. Any other PDFs will not be imported properly and thus cannot be edited, which is no surprise considering that Illustrator is not a general-purpose PDF editing tool. It might also be possible to do it in other software that supports Illustrator formats (like CorelDraw), but of course nothing beats the original.
Open PDF file Open AI file