The flaps were kept closed by a spring, they didn't stay up by themselves. But very soon the aftermarket industry found just the solution for that particular problem, like this device made by Accessory Engineering (photo taken from the book "Accessories for your Sports Car" by Larry Reid, published by Sports Car Press, New York, 1958)

You will likely never find one of the original aftermarket parts from the 1950's, but with a little creativity you might make your own.