We have seen a lot of problems with the injectors causing this type of problem. The following test will need to be done when the problem is happening.
Verify that the Purple/White wire from the Ignition module has a 0-5 volt square wave signal when it is a no start; if not, check the crank sensor output with an ac voltmeter. It must produce at least 0.6 volts ac while cranking. Check the injectors during no start. All 6 must be above 12 ohms individually, or above 4 ohms when checking 3 at a time. Verify that power and ground to the Electronic Control Module (ECM) is good, sensor readings are normal, and Purple/White wire is good to the ECM, as are the injector wires. If all OK, replace the ECM.