I'm pretty sure that they stay on for about the same amount of time that the 12v power ports stay powered up, ~5 mins. I do not think that there is any way to change this short of hacking up the wiring harness plug to remove the stock power wire and replace it with an ignition switched power source. Sounds like way more trouble than it's worth.
I'm pretty sure the buttons don't stay lit always. Park your car, lock your doors, and come back out to your car in ~15 mins to see if the buttons are still lit or not. My hunch is that they won't be.