Modifying PDF file changes permissions on network

While the guidance provided by ACP Radzmar is correct,  and also your observation is correct, you need to clarify a few more things about the current setup for that shared folder.

Which operating system is  doing the share?

Are all other computers accessing this shared folder participating in other network domains or restricted via group policy?

Where exactly is the shared folder? 

Is the PDF file stored in a folder under your current user profile, like "My Documents" for example?

Is the original shared file accessed simultaneously by more than one user at the same time?

Are these users' accounts enabled with read and write permissions to the shared PDF?

And even more important, what program are the users employimg to view and modify the shared PDF file? a web browser? Adobe Acrobat Pro? Adobe Reader? a third-party PDF viewer/editor?

All of these considerations are important because, even though the folder shares are managed at the OS level, Acrobat and Reader are tightly integrated with the Microsoft Windows File Explorer and the Internet Explorer security zones.

That said, it seems like you may be able to work around that by moving the shared file(s) to another directory outside of the current user directory and enable read/write permissions specifically for the users that will  need the access.

In addition, if your users are opening the shared PDF in Adobe Acrobat or Reader, they may need to disable Protected Mode at startup, Protected View, and possibly disable Enhanced Security (if the network is internal and closed with no access outside of it), to include customizing the sandboxing preferences in "Security (Enhanced) --->>> "Privileged Locations" by File, Folder Path, or Host.

Use this detailed Adobe Helpx guidance and see if you've missed a step:

• https://www.adobe.com/devnet-docs/acrobatetk/tools/AppSec/protectedmode.html