Dropbox and MS mail databases don't mix as you've found out. Outlook waits until you close the program to write changes to the database. The problem is the database is one file with everything inside it. The database can get quite large so the sync can take a while. If it's stopped in mid sync to DropBox it can get corrupt.

It is recommended that if you do back it up to DB you make sure that you first quit Outlook, then give DB a chance to sync. It's best to not trust it as you've seen.

DropBox also has a feature, if you go on their website to your account, they have previous versions of all of your stuff for the last 30 days so you may have a chance that a good one got backed up recently.

I don't know what else to do, sorry.