MIDI Notes, sync., MIDI Clock

I have Cubase as a sync master, with Ableton Live as slave. All the MIDI comes through Ableton Live.

While the transport is stopped, sending MIDI notes responds well, but are not followed with any note offs. So, all notes sent when the clock is stopped are hung notes.

Is there a way around this ? Certainly, if I’m not recording or playing back, I still want to be able to play my instruments normally.

Any ideas ?