Permanent hair dye is designed to provide long-lasting color that does not wash out. However, when applied to bleached hair, the dye may fade more quickly due to the hair's porous nature. Bleaching opens up the hair cuticle, making it more receptive to color but also more vulnerable to fading.
The rate at which permanent hair dye fades on bleached hair depends on several factors, including the type of dye used, the condition of the hair, and the frequency of washing. Generally, darker shades of dye will fade less quickly than lighter shades. Hair that is in good condition will also retain color better than damaged hair. And finally, hair that is washed frequently will fade more quickly than hair that is washed less often.