Just got back from a fake tan stain today approx. 2 x 2 ft in one corner of the room, think she must have just stood there to do an all over body tan.
Explained was a good possibility that it was permanent but she wanted the carpets cleaned anyway and said just do what you can.
Don't know if this will work for you, but applied a heavy spray of coffee stain remover to a small patch in the middle of it, left to dwell while I cleaned the rest of the room, came back and rinsed and the patch was considerably lighter than the rest, covered the rest of the area, dwelled, rinsed, then did the same again all over, Stain gone,
One very happy customer.