Steve,
I had this problem a few years back, a customer had dripped cooking oil all along the hallway from the kitchen. I went back to clean it about 3 or 4 times before it finally went. In that time I used several different cleaning agents, Micro-splitters, Eco Spotter, Blitz. With each one it would be clean but would re-appear weeks later. I put it down to having soaked into the backing and just kept wicking back up. I did not charge for the re-cleans but gained a good regular customer which has paid for itself many times over.
I guess if you could lift the carpet to clean the back etc you may cure the problem, but that is not always possible. Or if you have one of those spot lifters you could flood it with detergent and extract out, I probably would have used this method if I had one at the time.