So I came across this question on Etsy and tried to give a very basic explanation why some minerals are colored the way they are, and why some will fade when exposed to light/heat. I thought this might be something others would be interested in and thought I'd share what I wrote here :)
Color and fading has to do with the composition of the mineral. Basically what happens is when some minerals are exposed to sunlight/heat, the electrons get rearranged, resulting in color loss. This only occurs in some minerals, because there are different ways minerals can get their color.
Idiochromatic minerals have their color due to their chemical composition, such as malachite and azurite. Thus their color is pretty constant. Malachite for instance is always green - there may be varying shades of green, but never any other color but green. Were you to take away the component that results in the green color, you would simply no longer have Malachite, but some other mineral.
Malachite is always a shade of green.
Allochromatic minerals get their colors from trace impurities in their composition or defects in their structure. Fluorite and Quartz are examples. Therefore they're prone to color change - again it also varies from mineral to mineral as some are more resistant to others depending on composition and structure. Unlike with Malachite, were a trace impurity removed that caused a certain color (e.g. remove the iron and aluminum responsible for the purple color of Amethyst, which is a type of Quartz), you still have the same mineral (i.e. while the stone would no longer be purple, it would still be Quartz).
Amethyst is a type of Quartz that is purple due to iron and aluminum impurities.
Here's an article I found that includes a brief discussion on color loss in Fluorite - its a reprint from Rock and Gem magazine http://members.aol.com/Florspar/articleF1.html
And this one explains why minerals have color and a bit about color variety occuring in the same mineral http://geology.csupomona.edu/alert/mineral/color.htm
When I have time I'll try to find some more info on this :)
In the meantime, I recommend always storing jewelry out of direct light and away from sources of heat, so you can continue to enjoy the beautiful colors of your stones for years to come!