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).