I suspect you may need to get a fresh checkout from a direct access https URL derived by looking at Dropbox account in web browser, not explorer. Verify this with Repo Browser, and set user and password, etc, do checkout, and set new local directory to sync to wc directory on Dropbox as a backup, not primary. If nothing else, from web browser you can get a zip of the repo data and put it back on your machine.
Sorry, thought you could get a zip, but it only lets you download files singly, with basic Android client. The drive letters issue counts as a bug in svn, not tsvn. It's valid for wc tracking of revs, but revs in repo shouldn't have them because source persistence is not guaranteed; checkins can come from wc's on removable drives or over the net.