My activities hadn’t been syncing to Dropbox for a while (since mid-November 2014).
This activity was not synchronized to the following services: Dropbox: There was a problem indexing your activities on Dropbox, so no activities will be uploaded to Dropbox.
Everything else was syncing fine (Strava, Endomondo, Garmin).
A quick email to the author and everything is solved:
If you look in your Dropbox folder there should be a number of files with .tcx.summary-data extensions. Move those out of the folder and it should start working again – this is a rather ancient artefact of a mistake I made in Dropbox sync back in 2013, surprised it kept working as long as it did.
Delete any files with .tcx.summary-data extensions from your Dropbox folder.
*I only recently found out what that was short for. I’ve been ignoring it for years assuming it was invalid html markup.