Actually, the iPod continues to charge only until the battery is fully charged. Then it stops. So you may find that when you turn the car's ignition off that the iPod is still being charged - but - after a short period, the charging stops. After leaving it alone for a while, check the iPod's screen before turning on the car's ignition. If the screen shows nothing at all, then I think you will find that charging has stopped, since the screen will continue to show dimly all the time that the iPod is being charged.
I speak from experience. When I first installed my iPod Classic into my Mazda, I too found that when I turned off the ignition, the Classic's screen continued to show the charging symbol. But after a short while, it stopped charging.
Even if your iPod does continue charging, it will stop when charging is complete and that is probably why mine stops charging. Since you leave your iPod connected all the time, my guess is that it will be fully charged after such a short time that you do not need to worry about your car battery going flat. Unless your car battrey is weak to begin with of course.