Best not to hijack old threads like this, as the comments above might be well out of date …
The first thing I’d do is review the TROUBLESHOOTING chapter, SYNC ISSUES section of the outstanding “DEVONthink Handbook”. No need to repeat all that here.
I guess the next thing I would try, as there are few knobs to turn with Dropbox, is to give Bonjour a try, using the two devices on same network. Bonjour method is known to be more reliable and faster. In addition to the instructions in the “DEVONthink Handbook”, see supplementary information at Bonjour Simplified
Then, once syncing going well, then attack getting Dropbox method working.
Is there any particular reason why you are using a third party internet service for synching? Do the other devices in the synch “diaspora” really need to be updated when you away and aren’t using them?