Have a look at this thread:
That solved the problem for me in combination with a script downloadning the latest version of Dropbox, closing running processes and then starting the process up again after installing and applying the chmod string from the above link.
Full installer DMG from the official source:
When a new version comes out, updating the URL version number should point you to the latest file.
Verify this is an official source:
Write a script to download and install it locally or upload to JAMF packages as is and create a policy. Worked fine for me