@Charles191 , the way I understand it, your client - not you - is an Airbnb host who is technologically challenged and doesn't understand the basics of Airbnb's rules and regulations, thus he or/and you ended up cancelling many reservations, thus consequently Airbnb deleted his listing. What is your role in this, co-host, professional property manager ? You talk about "our listing" in the headline, but at the end of paragraph yiu call it "his listing". Not very clear.
in any case, this predicable outcome of getting delisted for cancelling many reservations cannot be blamed on a robot or careless Airbnb employee: it is up to each host (or co-host) to know the basics, certainly about cancellations. The scenario that many Airbnb customers are coming to your client's house this week is not possible: if indeed Airbnb deleted this listing, they will or have automatically cancelled all future bookings.
Coming here to the forum now, with a request to be called tells me that you also have a ways to go to study and understand Airbnb's set up and rules. Perhaps educate yourself in depth about all of that, then apply for co-host status, fill out your profile a bit, and reapply to have this listing reinstated. Good luck!