I just went through something very similar with one of my cats. She started getting picky (she is normally a very good eater!) and loosing weight. Blood work, x-rays were good, so at the end of April, we did a dental. She lost several teeth, but quickly started eating well again. For about a week. Then her appetite fell off, and she developed an abscess under her chin. More antibiotics, another dental, where she lost more teeth, more antibiotics, and finally, after two months, she is back to eating well and putting on some of the weight she lost. The vet said her remaining teeth looked good after the first dental, but when she went back in, there were some pockets forming around some of the remaining teeth
I hope you figure out what it is