Trivia story which does nothing to solve your problem: I have a pair of pink pants (made in Bangladesh, I think); they started out red and bleed every time I wash them; I can only wash them with other reds and I've had these pants for over 15 years; I can't even guess at how many times they've been laundered. My DH wants them burned, but I love them; they're thick & soft & comfy. I bought a green pair at the same time ... made in the same country; now they're a sort of pukey brown after being washed and bled for so many years.
If Retayne does not work magic, I think you need to find some other use for your red fabric and replace it with one that does not continually bleed. This sort of thing is how I learned the hard way to never throw away my sales receipts.
Bella Boo: What great detailed info. Thank you very much.