The colour of hair, like the vibrant colouration of a butterfly or moth, is 'structural'. In other words, the chemical structure of the hair gives it its colour. There is no dye to leach out. Butterfly specimens preserved in museums retain their colour (supposedly indefinitely) and the same should be true for hair.
However, the enviroment in which the hair is stored will make a difference because alteration of the chemical composition of the hair (due to reactions with substances in the environment) will secondarily alter the colour.
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx