Oh just tell me - this is a right royal pita! Yes this an Android 4.4 issue. However, I now have a new phone with 5.1, so theoretically this should not be an issue as Google allows writing to an external SD card with this version. But the code needs to be changed to do that, and almost all the pdf developers have failed to do this including the well known ones like Foxit. How long as 5.x been out? Grrrrrr.
I also use pdf forms for collecting data and the best of the apps was Repligo (no longer being developed.) But it stopped writing to ext SD card from 4.4 onwards.
The only app I found that will write to a pdf form AND an external SD is OfficeSuite Pro by Mobisystems. But it is VERY clunky writing to forms.
The last time I checked, the following will write to forms but will NOT write to an external SD in Android v5: Repligo, Foxit, Xodo, qPDF Notes (most promising of those tested), pdfMax.
Still, solved most of this on my old Galaxy S3 by putting CM11 on it. Still works great. But rooting and putting a different ROM on it will not always solve the issue. Some apps obviously just look at the Android version number and not whether the phone is rooted or have say Cyanogenmod on it, as I've had some apps refuse to write the ext SD card on the S3 saying it is using v4.4 therefore cannot write to an ext SD.
1eStar suggests writing to the Data folder, and it is a clodge of a workaround - that I refuse to use. That is the way Google wanted us to work in v4.4, but it is definitely not the way must people work and is why Google changed it in Android v5. My work goes into client folders & subfolders, just as I do on the PC.
End of rant :-)
If anyone finds really great app that does work please let me know.