http://www.dailymail.co.uk/sciencetech/article-2176368/How-grey-hair-sign-good-health--redhead-make-susceptible-illness.html
The study suggests that the production of red pigment is to blame. Pheomelanins, which produce red and 'rich chestnut' hues, require a chemical called glutathione (GSH). This chemical is also an antioxidant. The suggestion is that producing red pigment uses up the GSH leaving less to work their antioxidant magic.
Yet more bad press for redheads!