Could be a number of things.
When it faults:
Check for proper fuel pressure (approx 40 psi at initial key on.)
Check for spark including proper timing. Timing light comes in handy
Check for air (Crack throttle slightly while cranking).
At least one is missing. Once you know which is missing, you can focus on that subsystem to identify and correct the fault.
FWIW, fuel pump or CPS are both likely suspects, however, if you fail to follow a specific troubleshooting procedure, you're likely to just rely on luck alone.
Steve