The cigarette lighter socket should not lose power when you start the engine...at least not on a "normal" car like a Chevy. Standard disclaimer for other brands applies.
Wife has a Griffin itrip and it's a pain, it does turn itself off all by itself and needs to be unplugged and plugged in again sometimes to get it working after stopping the ipod.
The Monster transmitter she had always stayed set and working and never lost track of what channel it was set to, etc. kind of expensive, but it worked well, although eventually it lost a channel due to a flakey docking connector.
I have an older VR3 transmitter that does not power the player, it loses channel info when unplugged, but I leave it plugged in most of the time as it doesn't use much power.
Not sure why you shut off the engine when stopped for a short time, as you most likely don't drive a 55 chevy with a blown big block like I do
