I had a CTS that did the same thing and it was the crank sensor. The sensor was aged and once it got hot the signal degraded and the ECM no longer had a pulse to coordinate ignition with. The worst part was there was no engine code thrown. The ECM simply thought the engine stopped turning. It was easy fix - certainly the Rover V8 is different but pretty much all modern ECMs work with same basic foundation. If you have a scanner that can read crank position sensor feedback just have someone watch it while you drive - you'll see the signal break up, once hot.