Most smart key systems will let the car run indefinitely, or until it runs out of gas, etc, once the smart key is removed from range, provided you don't turn the car off.

This is done for obvious safety reasons. Imagine for example if a car just suddenly turned off while you were going over a major highway bridge with no shoulders, etc.

Also it protects against the battery in the key dying.

It also protects against your wife getting out of the car with the key in her purse while you drive back home after dropping her off.

You probably want to realize your wife has the key immediately, not when you are home miles away from the key :)

While I was driving a friends keyless car (he had the key) he stepped out to get something and the car flashed some lights to inform me I was driving without the key. It didn't turn off (thankfully). This is the correct behavior.

I once watched a friend's girlfriend throw his cell phone out of the car while on the freeway. Had this been his car keys I would hope that the car would not immediately power off (especially since I was in the car).