Interesting thread.
I'm not sure exactly what happens, but my guess is that somehow an index in it's internal database gets corrupted and then it sits in a loop there for some reason whenever it hits that file/folder.
We have used Dropbox extensively in our office across Windows & OSX for at least 2 years and have had this periodically (and randomly) happen on some machines. Although I can't recall it happening in the last 6 months or so.
There was a period where it happened almost fortnightly to someone in the office and we almost swore off Dropbox to something else.
The above has always fixed the issue for us. YMMV.
I've never noticed a problem with Dropbox. Of course, I'm not running tools that show me battery consumption of apps and such on my Mac. Battery lasts long enough that it's never been a problem to look into.
I also had trouble with early versions of Google Drive. Maybe it's time to give it a try again. The problem I had was that drive thought all of my files had changed every day and started syncing the entire Google Drive folder again. I removed it and haven't tried it again since.