I learned not to use Dropbox for things like Git repos. I'd have a fresh copy on one computer, and then have an older copy on a different computer. Sometimes I'd accidentally overwrite the newer code w/ autosaving on the older code. Now I'm skeptical that I'll be able to keep everything properly in sync on any sort of network-ish file system that is wrestling for control with my local file system.
Oh, I ran into the same problems, so in the end I decided to treat the Dropbox repo as a remote - create a bare repository in your Dropbox, clone it to a local folder, push/pull as you would any other repo. It's not optimal, but it's an easy way to get a private hosted repo.