I would rec to check the ASD relay. The Auto Shut Down relay supplies power to the ignition coil and injectors. If there is no power, there will be no injector pulse and there will be no spark from th ignition coil.
The asd relay could be bad. Or the computer may not be energizing the relay. IF that is the case, the inputs to the computer may be bad (possible bad cam or crankshaft position sensor) or powers and grounds. But lets not worry about that yet. Check for power when this happens and get back to me.
The ASD relay supplies battery voltage to the fuel injectors, electronic ignition coil and the heating elements in the oxygen sensors.
The Powertrain Control Module (PCM) operates the Auto Shutdown (ASD) relay by switching the ground path on and off.
The PCM controls the relay by switching the ground path for the solenoid side of the relay ON and OFF.
The PCM turns the ground path off when the ignition switch is in the OFF position unless the 02 Heater Monitor test is being run.
When the ignition switch is in the ON or Crank position, the PCM monitors the crankshaft position sensor and camshaft position sensor signals to determine engine speed and ignition timing (coil dwell).
If the PCM does not receive the crankshaft position sensor and camshaft position sensor signals when the ignition switch is in the Run position, it will de-energize the ASD relay.
Just be sure the timing belt did not break and that the cam and crank sensors are good!