Thanks you for the details. i am going to try this suggestion first to see if it works
Are you able to exit Dropbox, delete the cache contents, then run a virus scan on your local Dropbox folder?
EDIT: It might be a false positive stemming from partially downloaded files that falsely triggers your antivirus, that is why it keeps downloading, Dropbox is trying to sync and that bit keeps being tagged as a malware and removed.
Solution:
Set the cache folder as an exception to scanning. Malware cannot run unless executed by a human and most people will not go into the cache folder to open files. Just ensure your antivirus is still active on your actual Dropbox folder and it should be fine.