
As Baruch Sterman pointed out in a lecture on Tekhelet, the molecular difference between Tekhelet dye and plant indigo is that Tekhelet dye contains Bromine.
My hypothesis is just like soy milk helps plant indigo better resist UV fading effects of the sun, the Bromine in Tekhelet does an even better job of helping Tekhelet dyed wool resist the UV fading effects of the sun.
Of course it is only a hypothesis until rigorously tested in a lab.