the "pro" said that the carpet has too much "soap residue" in it and it looks bad. Then he said his maintenance man confirmed that there looks to be too much "soap". He then said "I really hope you guarantee your work and can come fix this for us". 4....Months...Later. In a vacation rental, on the beach, that sleeps 6. Sun tan oils, sand, blacktop parking lot. All of these rentals get dirty very quickly. Lots of property managers have me on quarterly and bi-annual cleaning schedules.
I know this post is long, but might be worth a close look.
You've already got a ton of good advice on how to deal with this. I can only add that nobody, no matter how professional they think they are, can just look at a carpet based on how dirty it is and say, "Yeah, there's a bunch of soap residue that's causing rapid resoiling." I've been cleaning over 30 years and I can't do it, not JUST by looking at it. I do have other ways. My best guess is they said that because they thought it soiled too rapidly after you cleaned it. Crunchy carpet fibers are pretty much a dead give-a-way of heavy residue. Carpets that have been improperly cleaned in the past and heavy uses of spotters like Resolve or spray and vac type cleaners also can cause issues that absolutely WILL NOT EVER respond to a normal cleaning.
That's why ACID RINSES CAN AND DO help in many instances. Acid rinses are my preferred rinse, but specially if I know there is a residue problem. Clear water may be fine 90 + % of the time, but not always IMHO.
Then we have all the millions of sq. ft. of oil loving polys out there that will soak up oily substances like you mentioned like a proverbial sponge. My best guess is that's what was really going on here and these rentals need a minimum quarterly cleaning. Even acid rinsing will do little if anything to help that situation, but at least you can say with honesty that you've not left a soil attracting residue on their carpets.
I would have quickly, but calmly ask the person who called you exactly how the "pro" and the maintenance man determined there was soap residue? Did they take the ph or do anything other than just look at it and proclaim w/o any evidence that there was soap in the carpet? We all know, or should know, that soapy residues DO cause rapid resoiling. We all should also know that soap residues build up over time from improper cleanings or even improper spot removers.
They CANNOT easily be removed by a single cleaning!!! Resolve comes to my mind BIG TIME!
Does their house keeping or maid service use anything on the carpets to maintain appearance between cleanings? If so, what? Acid rinsing removes these residues FAR, FAR BETTER than water alone. Don't agree if you want to, but you'll never convince me I'm wrong on this. Perhaps some of this might help to better handle such a situation and not wind up doing a free cleaning OR getting a bad review for no good reason.