The implementation of the REx is to try to maintain the battery level at nominally 6% if you haven't modified it in the USA...it does not stay on to build charge higher than that, but will stay on under some situations when required to maintain it. Descending a hill, the load is minimal, and regen is often capable of maintaining, and maybe even increasing the SOC, so the REx may not be needed, so it does shut off.
The implementation of the new 7-series plug-in hybrids just announced, allow you to charge the traction batteries from the engine to any value, up to 100%, so you have that full when, say, you get to the city for running around there only on electrical power. In that implementation, the electric motor can drive the car exclusively, but it is often a hybrid, where the engine is fully capable of driving the car at speed while also recharging the battery pack - lots more sophisticated and costly.