Maintaining power to a car FM transmitter

[Billfred]

No, not that FM transmitter.

I own a Griffin RoadTrip transmitter for getting my iPod to play on my car stereo. I also try to keep my engine off when I know I'm going to be stopped for a couple of minutes. The problem comes when I restart my engine--the cigarette lighter (wisely) loses power when I turn the key to start, which causes the RoadTrip to shut off, which means I'm greeted each startup by gratuitous amounts of loud static from my stereo.

The slacker approach would be to find an FM transmitter that worked off of my iPod's battery or an internal battery. Aside from being a nerd, I don't see a good reason for tossing a perfectly good unit.

The nerdy solution, it seems, would be to find some way of storing enough energy to allow the RoadTrip to remain powered for two or three seconds when power from the cigarette lighter is lost. I'm not sure just how much juice the RoadTrip requires, though I imagine it varies according to the iPod's charge state as well (as the RoadTrip can charge an iPod through the dock connector). Regardless, the cigarette lighter is fused for 10 amps at 12 volts. Anyone who's been in or around my car will attest that there are no points for style.

What general approach would offer the best chance of success? What kind of precautions would need to be undertaken to protect the other things in the car beyond the obvious ones you learn from building FRC robots? Or am I just better off mashing the power button to turn it back on each time I restart my engine?