Can you confirm you are on version 4.0.1? I only confirm because some users are not aware it is out.
If so all you have to do is make sure the MIDI Start is being sent when restarting BB. I believe you may not be able to make this work if the BB is set to mute pause. The BeatBuddy should use a normal pause to send the Start command right as it unpauses and stay in sync.
Can you confirm you are not currently using mute pause?
Let me know thanks