"Natural rubber," he began, "is made of polyisoprene chains that slip past each other when the material is stretched. When raw, the substance is too sticky and soft to be of much use, so it is toughened with the addition of chemicals, like sulphur, which creates cross-links between the chains, making the rubber stiffer and less sticky. According to all the "How It's Made" episodes this kid has watched growing up, this process is called vulcanization.
"Over time," he continued, ultraviolet light and oxygen in the air react with the rubber, creating reactive radicals that snip the polyisoprene chains into shorter segments. This returns the rubber to something like its original state - soft and sticky. Meanwhile, these radicals can also form new, short cross-links between chains. This hardens the rubber and eventually it turns brittle (see above photo). Any vulcanization agents left behind, far less cunning than ninjas, (he chuckled over his clever aside) contribute to the process."
But wait! He wasn't quite done ...
"Whether a rubber band goes stick or hard depends on the relative rates of these processes, and these rates in turn depend on the rubber's quality (additives, fillers, dyes) and how it is stored. Heat and light speed up the reactions, and the presence of strong oxidizers such as ozone creates even more radicals. The fate of all rubber bands depends on the temperature in the room, and on whether you have a desk by a window or near a machine such as a copier that creates ozone."
Elucidating, he offered this final bit, "Polymer chemistry of rubber is pretty messy, so it is actually difficult to answer precisely. If we put some rubber bands in the refrigerator, the chemical reactions would be slower, if we put them on top of the desk with the light shinning in on them, it will speed up. The reaction rate is about double if an 18°F rise in temperature. Of course, we can't forget quality. Designer rubber bands have a different chemistry than inexpensive office brands. There are so many factors, including whether or not the rubber band was stretched out in a rubber band gun, that really, I just can't say precisely why these particular rubber bands melted."