You certainly can keep a yellow tang. ( if I can anyone, can)
I had a similar issue with clown fish long ago. Adding frozen food to their diet was the key for me.
What do you feed your fish? You said you have a cleaner shrimp.
I would not keep tang without these useful creatures. I prefer to keep two.
There are two yellow tangs in our senior center tank. One is larger and was the first tang in our setup. It didn't look real good in the store. Good color, but very thin in the belly. This fish has been with us several years now, it still looks thin more often than not, but it seems to be in good heath otherwise.
We added a smaller yellow tang a couple years ago. It was fuller bodied , and continues to usually be a bit thcker than the larger tang. This tank gets a cube or two of saltwater multipack twice a day, and nori two to three times a week. So I don't really have any trick to show you, but maybe there is something in there that helps.
Sometimes fish die and we really don't know why. Don't give up on the yellow tang.