Interesting! These are just my ponderings. I have no solutions... sorry.
So when they say print... they are actually printing from a FileMaker layout.... rather than opening the PDF and printing.
Previously I have experienced problems with Windows and pdfs that was essentially an active window / active program thing. FileMaker might appear active and respond like it is mostly active but it is not until you completely leave and return that everything becomes active. Windows has never managed PDFs well because the readers are not as integrated into the OS as on the Mac.... so the external PDF reader is used in the printing process and not properly being released for FileMaker to become fully active again.
Are you scripting the whole print process including stuff like preventing abort and suppressing error messages?
Have you tried forcing the active window by selecting and bringing to front with eg a go to object...?
Have you got a halt script or exit script at the very end? It may be that your script has not completed... (who knows?)
Could it be there are preferences for the PDF app that could effecting printing.
On a Mac, I might use Applescript to reactivate FMP if nothing native in FileMaker would work... but I would exhast everything FIleMaker first.