Can't add much more, getting any fault codes read would probably be a good start. Any cheap basic EOBD/OBDII code reader will help diagnose any engine problems, but they will only connect to the engine ECU, and not to any other systems on the car.
If you get air in the system, it should bleed itself through the injectors.
Is it a cough-splutter type stop, or a dead cut out?
Possible fuel starvation, as Jocko says. Could be fuel pump, fuel pump relay, fuse, blocked fuel filter, etc.. Could also be something unrelated, crank sensor maybe, this should show up as a trouble code.
Also consider immobiliser - I'm not sure if the Jazz immobiliser cuts ignition, or fuel pump - some cars which cut the latter exhibit similar symptoms when the immobiliser is not disarmed.