This is the result of limonene from the orange dissolving or weakening the rubber balloon. Limonene is an essential oil that is present in orange peels in fairly high concentrations (the pure compound smells very strongly of orange). Limonene is a colourless liquid hydrocarbon. It is used in chemical synthesis as a precursor to carvone and as a renewables-based solvent in cleaning products, and as such is quite flammable and you can even start a fire with an orange, seriously!!
Original link: http://www.youtube.com/watch?v=Uhd3gIJn034