Certainly a flaw in Dropbox, but one that can be easily worked around I think. Don't put the .pst directly in the Dropbox folder. Instead set up a scheduled task/cron job to copy it into Dropbox every few hours.

The Outlook .pst file plays notoriously bad with backup and synching in my experience. I set up CrashPlan for a family member once, and when I followed up a few weeks later it hadn't backed anything up in weeks because it was stuck on the .pst. In this case it was because the .pst was so huge and kept changing so frequently. By the time it had been uploaded for off-site backup, then it had changed and CrashPlan would start uploading it again. CrashPlan wasn't smart enough to prioritize other files in between, probably because it puts the most recently changed files in front of the queue or something.