I started a hybrid drive-bike commute in May, 2013. My Prius has a trunk-type bike rack with nylon straps that is almost always on my car. In fact, one of the nylon straps broke a long time ago (10 years?) and I simply tied it in a knot and kept using it. When I started bike commuting, I briefly contemplated buying a new one but decided against it.
So, fwiw, my bike rack has been on my car nearly every day for almost two years and for long drives and short ones (I drove about 250 miles with it yesterday -- from Richmond to DC and back).
Never had any issues. I supplement the straps that keep the bikes on with bungee cords.