A customer of TeamDrive just forwarded us a response from Dropbox support regarding the same issue:
Thanks for contacting Dropbox Support!
The latest version of iWork (upgraded with Mavericks) changes the way files are saved. Instead of individual files, changes are now stored in file packages (archive folders). This prevents the Dropbox application from correctly synchronizing those changes. Our engineers are aware of this issue and are working on a fix to synchronize the new iWork files, however we can’t give you an exact timeline on when this fix will become available.
Currently, the only workaround available to keep these files in sync is to downgrade to the previous version of iWork. To downgrade you can go to your Applications folder and install the previous version of iWork by running the installation file in the iWork 09 folder that the upgrade should’ve left in place.
We apologize for the inconvenience this might cause. Let me know if you have any other questions or if there's anything else I can do.