When driving-engine shuts off - like key turned off--No Codes!

I am a Home grown mechanic - retired & have learned computer systems. yet!!- Not extremely experienced daily with them! I bought a 2003 saturn vue for daughter. Seller did great maintaence on it 1 ownwe since new. The car (owner had same problem) will start & drive fine as should. Within 4-6 miles (heat) engine will shut off -just like key is turned off! I have actually restarted the engine while still rolling to a stop in neutral! whll do same -sometimes soon & sometimes after a few miles again!. NO CODES!! EVER!! I did replace the Crankshaft sensor(from experiences in past) still the same condition! On live scan - all looks great till engine stops! I am leaning toward replacing the ECM - engines computer. Your take on all this? Thanx.