The car bra's dont move around, not decent ones anyway, but they're not designed to be left on permanently, obviously dirt will build up (particularly if it never gets washed) and paint will rub, they're designed for longer trips where stone chips occur from driving behind vehicles at speed before overtaking. They should be washed if they get dirty and this is easy. Its nice soft felt on the underside.
I had one and used on trips from Adelaide to Melbourne, worked perfectly. Not a single scratch or chip on my car, sold it at a good price (above redbook value) and now the car bra is up for sale also in the for sale topics.