Even though I see that you have replaced it, that really sounds like a bad CPS. Run your codes and see what comes up. Also, I have never heard of this happening on an SHO but it's food for thought. When many of the GM electronic ignitions start to go bad (usually a problem with the distribution block similar to SHO's DIS) the engine bay gets hot and warmed up to running temp the distribution blockshorts out (because it's just made of plastic and absorbs the heat easily) and causes the same problem you describe (most notably on some of the older quad 4's and 3.4's). Like I said, I've never heard of this on an SHO but if the CPS is newer you gotta start thinking of other possibilities. .