Once the car is running you can take the fob out of the car will not stop. I think they do it for safety reasons, once the car is running you don't want it to stop just because it doesn't detect the key anymore. What if you were on the highway driving in traffic and the car for some reason doesn't detect the key in your pocket anymore, would you want it to turn the engine off?
My wife has a Hyundai Santa Fe and on a few occasions I have driven her to a store and when she gets out, with the key fob in her purse, the car just beeps and flashes the "key not in vehicle" warning on the dash but the car keeps running. I'm able to drive around the parking lot looking for a parking space while she is in the store with the key. If I turn the car off it obviously won't start until she comes back with the key, but it keeps running otherwise.