I always run with my face shield in the up position. It isn't bad until you spin the car and rubber and dirt covers the entire inside of your car including your face (voice of experience).
Whether there is any truth to it or not, I try to run with the top down as the body goes through a lot of twisting and I don't want to bend the frame of the convertible top. Once again, I don't know if there is any truth to this... besides, its more fun to run with the top down.
