I think there are a lot of things that could be going on here.
Firstly your temperature. What is it?
What about phosphates levels? There are indeed fish that are quite sensitive to phosphate levels.
I'd also be on the look out for your KH
levels. They are suposedly meant to be important only to inverts such as corals, but since it has such an imporant effect on the buffering capacity it is important.
All that being "okay" I would look at the way you introduce the fish. Whenever I introduce a fish into an aquarium I have it in a one of those plastic transport bags, and then leave it in the water for around 30 minutes to allow for proper temperature changes to take effect. I then add a cup of water from the destination tank into the bag and wait another 30 minutes. I do this cup of water trick three times. Yes it does take significantly more time, but the stress on the fish is reduced greatly.
After that I would look at any other stress causes. Lots of vibrations, more so sudden ones than anything. I would also look at there being a disease or parasite.
Being a reef tank, you are going to be limited in your medical applications. If it's whitespot, itch or velvet I would recommend something called Tri-Sulpha (or tripple sulpha). It nuked the whitespot I had after about a week and I have corals an anenomes. You must be very careful about what medical remedies you add.
Even after adding these remedies I would wait for about a 4-6 weeks before adding anything.
It may also pay to add some Stress Coat and Melafix. The stress coat will nutralise some of water nasties, and also help restore the protective slime coat to the fish. The Melafix is like a general purpose anti-bacterial remedy. It's quite effective and is reef safe. In fact the marine stores I speak to say they add Melafix to aquarium that has new inhabitents, and this occurs weekly. You don't have to do it weekly as they are a pet store with huge turnover of inhabitents.
Also, water changes from a reputable source are essential to clearing up such mysterous problems. I would also add some activated carbon to help absorb the micro compounds/elements. The quality of the active carbon is also very important.
Do you have a protein skimmer?
A quaranteen tank is the best idea for new inhabitents as well.