I too am sorry for not seeing this thread sooner and hopefully the poster will return. My Basenji had some teeth removed and the vet prescribed Carprofen as the follow up antibiotic. My Basenji turned out to be allergic to Carprofen which caused her liver to fail. I went through the same scenario you are describing. She gradually quit eating over the course of several days and then her water consumption started to go down. The eating had me worried since she had an excellent appetite upon return from the vet and the final purging of the anesthesia from her system. Nevertheless, her condition started to degrade. I followed her outside and watched her urinate. Her urine was a very bright yellow. I suspected then a liver issue. Once back inside she was shivering - off to the vet we went.
LIver panel blood work up showed very high on specific indicators for failing liver. Vet prescribed Denamarin (containing SAM-e and silybin). SAM-e helps protect liver cells from cell death and aids in cell repair and regeneration. The Vet also started fluid injections. Fluid injections were everyday for two weeks. My Basenji showed a remarkable response to the fluid injections becoming much more her normal self even after the first day. She hated the injections and I could hear her cry when receiving them at the vet (believe me that will tear you up). But she was doing better and she (me) were going to have to tuff this out. Also a different antibiotic was prescribed to prevent liver infection during recovery.
The Denamarin comes in dosages based on weight (medium for us). It is the size of a large human like solid oblong vitamin pill. Instructions want you to give it on an empty stomach and preferably not to cut it or place in something similar to a pill pocket however you can if necessary. My Basenji would not take that size (can't blame her). Cutting and disguising it did not work either. I was frantic and got the SAM-e in powder form. I couldn't slip her that either. All though some folks had success with peanut butter and liverwurst.
I finally after three days had to have the vet pill her along with her fluid treatments. A week later another blood sample and her liver panel indicators were coming down. The pilling would last for a month and it took two people to get the pill down her. The important part is - she fully recovered from the liver failure. She is 13 1/2 yrs old.
My experience after having 5 Basenjis is that the breed is sensitive to medications (anesthesia also). Many of the medications work just fine in most other breeds and mixes. The vet, if not that experienced with the Basenji, must be cautioned. Mine was not. Before accepting any medication have the vet go over any contraindications with you and to double check their resources for potential side effects when dealing with Basenjis. They may switch to something else if a medication has a bad track history with Basenjis.
Know what to watch for should your Basenji start to react in a non-positive manner. The poster did not indicate if there were medications in play when the dog started showing degenerating conditions.
I sincerely hopes this helps in some way and helps other Basenji owners