Is purple paint more susceptible to UV damage than other colors?
I would also agree with you and the comment from ssavec. The only point that I would make is that it shouldn't be because of the colour of the pigment only the stability of the particular dye it contains (almost certainly organic). In fact the colour of the paint should make it less susceptible to fading as it is reflecting colours at the violet end of the spectrum (subject to your definition of purple) rather than absorbing them.