I also want to recommend the Aveda conditioner for red hair Madder Root Color Conditioner > Conditioner > Hair Care > Aveda
I mix a tablespoon or so with my regular rinse out conditioner about once a week - it really helps keep the color vivid. I wouldn't use it alone - I think it would be drying.
If you use it, be sure to wipe up any spills - it stained my tub when I forgot to wipe up a drip. Not so good for the tub but that kind of staying power is what you want for your hair color!