Dyes differ from pigments because they dissolve easily in the vehicle or they are liquids themselves. They are used in markers because their solubility helps them disperse through the felt tip by means of capillary action.
Many dyes are susceptible to fading, but it all depends on the particular colorant, and in the older packaging, they don't tell you the colorant.
In this test strip made from a few older (early '80s) bottles of Dr. Martin's dyes, the violet color completely vanished.
The molecules in older synthetic aniline dyes were especially fugitive, or susceptible to fading.
However, recent technological advances have improved Dr. Martin's and other brands of dyes. They generally now use micronized pigments rather than the more vulnerable synthetic anilines.
Many of these same improved dyes are used in staining leather or wood, and they're much better than they used to be.