Car sounds a warning as soon as the fob leaves the cabin. Just ask my wife who's had to listen to it chime when I've run back into the house to grab my wallet or sunglasses after backing out of the garage. Not sure why the bike doesn't care.
Note that while the car sounds a warning, it DOESN"T shut the engine down. That would be a totally unacceptable and downright stupid thing to do on purpose, thus even the less intelligent car companies don't do that. And I'm pretty sure even the folks at H-D wouldn't do such a thing either, but can't guarantee that one.
I assume with your car this warning chime eventually times out, kind of like many seatbelt alarms do. If not, and the battery in the fob or the fob itself dies in the middle of a trip, hopefully the manufacturer includes a set of earplugs. I could see having a warning light illuminate if the vehicle loses the signal from the fob, but for whatever reason Harley didn't think it was necessary from 2007 until Rushed More came along. And if I understand how the late models work, they still don't keep a warning light illuminated continuously. I could be wrong on that one.
Regardless, keeping a spare fob battery with each of a person's vehicles would be a good idea, now that the vehicle manufacturers have all allowed the electronic gadget freaks to take over designing their products. I for at least one prefer the good old fashioned ignition switch and key, and a pushbutton fob for unlocking the doors. It's pretty hard to forget your keys and fob on those vehicles, and you don't have to worry about folks stealing a constantly broadcast signal and using it to unlock your car and drive away. That last part is already being done in this country btw.
Sometimes "progress" really isn't, and sometimes supposed conveniences like not having to unlock your doors and insert a key into an ignition switch are more trouble than they are worth. But for easily fooled people, those ads on TV showing people walking up the back of their SUV with arms full of packages and just waving their foot under the bumper to open the liftgate are a real selling point. I'm amazed when I hear people discussing new cars and the only thing they find important is the electronic gadgets and infotainment system. You could sell these people a complete mechanical nightmare, as long as you give them the latest toys.
Rant over for now.
Jerry