Proximity key question ?

[BDayks]

So today I had to do some car juggling and I had my SO start my car up for me. I was rushing around to get going so i wouldn't be late. I started moving the cars around so I could get out and I set off down the street get half way down the street and turn the corner and I see a message No Key detected. I couldn't do a u-turn so I went around the block and back no issues other than the message and a few notification dings. Now my question is that all that would happen if I didn't lock my car and someone jumped in and drove off ? I guess if you turned it off you couldn't get it going again but is there a distance to how for it can go without the key? I seem to remember an episode of Top Gear and they did that with a dodge and a proximity key as a joke and it turned off after a set amount of distance (Unless it was for the show).   

[SHOdded]

Time to change the fob's battery:
http://www.ecoboostperformanceforum.com/index.php/topic,3030.html

IDK, I'd assume that at the very least any time the car is in P/N, the systems would check for the presence of a key before allowing gear shift/motion.

[Dxlnt1]

Some security features on some new cars allow for car to be driven approximately 1-3 miles before shutting off. This was in response to car hackings. SOmeone thought it was a good idea to let culprit get a safe distance way then stall car out.

[BiGMaC]

It's the battery in the fob as Manu suggests.  It's exactly the intermittent behavior I started seeing on mine... replaced the battery and all is well.

As far as the distance, I guess once it's started it will go until you turn off the engine....
in my son's MKS he started it, got out, put his fob down in the garage, got back in and drove across Phoenix.... then discovered no key fob when he couldn't lock it... I had to take him his key fob so he could stat it after work.