First, I'm very glad to hear you use a quarantine process. Very important for all marine specimens, especially tangs.
You didn't mention how you treated the fish for Marine Ich. Hypo? Copper?
In a quarantine tank, controlling water quality is a challenge at best. If you used a hyposalinity treatment, controlling pH is hard. If you used copper, it is a poison and not 'tang friendly' in general.
Without a visual sign of any microbe, I'd say the fish is more or less responding to one or more water quality issues. Use vitamins in its foods. Include beta glucan in its food while it is recovering. Check for waste organics hiding about and remove them. Test water frequently for ammonia and nitrites. Unfortunately, there are other things that go wrong with our aquarium water which these tests don't show. So, to handle those, do large water changes every day, making sure the water is pH adjusted; salinity adjusted; and temperature adjusted before making the change.
If the fish doesn't improve in a few days with the above care, consider it a bacterial infection that should be treated with an antibiotic.
