Why does the colour of amethyst fade if exposed to too much light?
The reason why amethyst loses its colour in sunlight is due in no small part to what impurity in the $\ce{SiO2}$ crystal structure gives the vivid purple and violet tones of amethyst.

According to several sources (1),(2),(3), the main source of the colour is naturally irradation-borne tetravalent iron $\ce{Fe^{4+}}$, which is formed via naturally occurring gamma radiation altering trivalent iron $\ce{Fe^{3+}}$ during crystalisation (3).  Other elements exist as impurities but are far less important considerations for the colour produced (3).

The tetravalent state of iron is inherently unstable in 'normal' surface conditions and the process is reversible due to prolonged exposure to natural sunlight (3).  Some research and experiments have demonstrated that some of the bleaching is caused by the UV portion of sunlight (4).

References

(1) Amethyst, Mindat.org

(2) Dudushenko et al. 2003, What Oxidation State of Iron Determines the Amethyst Colour?, ICAME 2003

(3) Hatipoğlu et al. 2011, Spectral, electron microscopic and chemical investigations of gamma-induced purple color zonings in amethyst crystals from the Dursunbey-Balıkesir region of Turkey, Radiation Effects and Defects in Solids: Incorporating Plasma Science and Plasma Technology

(4) Nunes et al. 2013, Spectroscopic study of natural quartz samples, Radiation Physics and Chemistry