Dear Car Talk - car’s computer thinks mom’s a thief

I read you column in the Fort Collins, CO Coloradoan. As a car hobbiest, I am looking to learn and maybe out-guess you. I think you missed the mark in the Car’s Computer Thinks Mom’s a thief.
My first thought of why the car “turned off” was reinforced by my second reading when Mary wrote “She then has to turn the car off, TAKE THE KEY OUT…”
How about Mom, after having the electronic key, maybe with a weak battery, serve its purpose (opening the door and starting the car) puts the key in her purse and then the purse on the passenger seat or floor, or otherwise out of range to the sensor.
To me this reasoning yields the described results and also the behavior of an older woman.

The passenger seat is not out of range of the sensor.