What's your MIDI controller? Have you tried checking what's really being sent by the controller?
Some controllers (like M-Audio) use "Note ON Velocity=0" as their "Note OFF" which are 2 different MIDI codes (0x8? vs 0x9?)
But, I've tried both types of MIDI controller keyboards with Matrix-12 and it works fine, both as Standalone and Ableton Live.
...I can check this again, just to be extra sure.