I've been having conversations with Venmo through email for about 2 months now regarding this issue as well.  Strangely, it randomly connected and downloaded transactions just 3 weeks ago but has failed to sync since then.  I just got an email today from their customer support team and they said that this feature is not supported and even more strange stated that it has never been supported.......Well, I've been syncing just fine for the 8-9 months prior to the issue.

Anyone get any updates on this?