Started having this issue recently on my Paperwhite. I also tried using a "shared by link" folder on Google Drive. That loads the list of items in the folder, but won't download the files to the Paperwhite.
The only workaround for the paperwhite I've found is to download via my android phone and save it on the kindle via USB. When travelling, I now just download the calibre papers to my phone or Nexus 7 from the Dropbox app, and read in the Kindle app. That rather defeats the purpose of having a kindle now doesn't it! Guess my kindle is obsolete
Sigh...