What colourline are you using and what level is the clients base? Is her natural base reddish brown or is that the left over residue from previous colours? It just seems like a lot of missing information we'd normally require to give you advice.
i use goldwell but can use another line... she is gray but i have been coloring her trying to get her to a purple... which as i said fades to a red brown always... i have used nutrients also but it goes to a brunt red
What after care is your client using? If her hair keeps going red you could get her to use something like Fanolas no orange. Red+blue= purple. She may be using something at home that strips the colour. I would also suggest that she use dry shampoo in between showers. I would use a cool toned purple (there are a lot of warm based purples and cool based). If you can add just a dot of green into your mix (not even the size of a pea) then you have created a cool based purple essentually.
I would use a semi / crazy colour or even a hi lift pure tone (some brands have these ) with low peroxide or water on the ends and make sure she is using a colour shampoo , not swimming or washing her hair everyday all these things will help .I'm not sure adding blue would help it might make more brown looking when it fades .
Whenever I did this with wella I always added a spot of 0/88 blue intensifier or 0/28 matte blue intensifier as I always found wella purple shades to fade to red. This helped a lot.
If this still doesn't work for you then it may be worth considering prelightened the hair so there's no red in the hair and then use a direct dye to give you the exact shade you want