The CPS will not stop the starter from engaging.

Here is my advice, wait for this to happen again:
When the car refuses to crank, relax the key to the ON position.
If, in about 30 seconds, the engine fan warps up to high speed, then the ECU is not powered up and this is usually the RCM but COULD be a failed output from the key switch (but I doubt that).
If the fan does not speed up, I'd wonder about system voltage. Low voltage will cause the engine to cut out AND cause a no crank as well.

Usually, you'd have a battery (alternator) light in this case but not always. Also, being ready to check system voltage when this happens (carry a meter) would be helpful. Crossfires will not crank below about 10.8 volts.

That's all I can come up with.