As a former LAian and current SoCaler, I find it odd that LA has so many convertibles but on a relative basis, so few people drive top-down. Not sure that I could quantify it, but it was enough to notice. Have other LA people noticed this too? I guess it's because of the very real possibility that you can get hit by a stray bullet driving through some parts of town.
I have always owned convertibles and always lived in L.A. and in the last 10 years the top is definately staying up more frequently when driving in town. As trafffic congestion becomes worse, it becomes really unpleasant to have the top down in the broiling sun, inching along, surrounded by fume-spewing diesel trucks and buses, and cars with their stereos blaring.
I now reserve my top-down driving for off-peak times and more pleasant and condusive environments like Santa Barbara, San Diego, Palm Springs, etc, where you can be on the (somewhat) open road with the wind in your hair.