(ETA: I realize you're talking about purple, but a lot of the red dyes are purple-based, so I'm assuming they work the same way, and I wrote my reply accordingly)
Okay, if you've colored with red, the saying is, your color is already leaving your hair the moment you step out of the salon. I color my hair every two weeks because the gray grows in quickly. I use a copper red that, if it fades, is a coppery brown that I can live with until the next coloring I can offer you these insights, learned the hard way:
1. If a shampoo has 'Sodium Laureth Sulfate' or pretty much anything 'sulfate' in the ingredients, your reds and burgundies will wash right out. Doesn't matter if it says the shampoo is safe for color, or if it's the $30 bottle of Highly Touted Celebrity Shampoo That Is Safe for Color. Sulfate = red running down the drain. Don't let your salon sell you stuff that has sulfate in it, if you want to keep your color longer than your first shampoo.
2. Get yourself a boar bristle, or mixed boar bristle brush, and brush your hair and scalp, at least 100 strokes a day. This helps pull the oil from your scalp through your hair, and keeps it shiny and your scalp invigorated. And doing this offsets the next part, which might worry you a bit...
3. Don't wash your hair as frequently. Right now, I shampoo twice a week. And brush, brush brush your scalp every day. If my hair feels very dry, or like it needs a boost, I will 'wash' it with cool or lukewarm water, with my head flipped over, and I really scrub at my scalp with my fingertips.
If you shampoo frequently, this will seem all wrong, but once you get accustomed to the idea, you'll be surprised how much healthier your hair and scalp feel.
4. For conditioners, I haven't noticed that any one conditioner is better than another, it really depends on your hair type.
Some shampoos that have been consistently great for red: L'Oreal Everpure is great for NOT fading color - but I stopped using this and their accompanying conditioner, because the dimethicone makes my skin break out.
I currently use the Giovanni 2Chic Ultra-Repairing shampoo, but I think that if I used it more than twice a week, my color would fade at a quicker rate.
I would love to know what other red-by-technology ladies use for shampoos and conditioners.