In my experience Dropbox won't sync if the local system time is too far off. Makes no sense IMO, but that seems to be how it works.
If the time is just used to check for certificate expiration, maybe nobody considers it worth worrying about. Which I guess is fine as far as it goes... but the other day I couldn't get Dropbox to do its thing when my clock was only a few hours off. It didn't seem likely that an SSL date check was involved in that case.
It's a common thing on school/university computers, where for various reasons, system time is always wrong and it requires Administrator privilenges to change it (I can't understand why).
IE, Unix time started then.