Like other programs with a database backend (i.e., Quicken, Outlook, Word, etc.), it's not feasible to open the database only when accessing it. And SQLite (the database engine used by UR) only locks the database file when writing to it (see here for minimizing database updates:
http://www.kinook.com/Forum/showthre...?threadid=3728). Most backup software is able to backup in-use files, but if Dropbox can't, one option might be to backup the file using a program that can (see
http://www.howtogeek.com/howto/windo...ed-in-windows/), and have Dropbox sync the backup copy.