Because I only have one computer and no mobile devices— therefore I only have one copy of the password database, and I need the password database to access Dropbox.
The sync folder is encrypted—is there some risk I'm not seeing?
Personally, I don't believe in leaving something like a password database exposed. That's akin to leaving a safe in the street. While someone might not be able to get in right away, why make it easier?
For you, I would just keep a copy elsewhere (friends computer etc.) or just get an additional device (mobile or otherwise).
The sync folder is encrypted—is there some risk I'm not seeing?