Ok here's what I've got in the old notes. If you have sync, the indicates the PCM is seeing both the Cam and Crank sensors and timing is acceptable, however if you're mising FICM sync one would first assume you would be missing the signal between the PCM and the FICM. Now that maybe wrong but from what I can recall it's correct.
Now when the fault occours, do you have a CMP_F pid reading a fault is present? If not I would venture to say the CMP signal is good and the PCM can see it. Also when the no start concern is present, can you see a cranking RPM?
I realize you have no known test units handy but it sure would be helpful right about now.