Sounds like ph shock. The ph in the lfs can be quite differant from your home tank, especially if the anthias was held in a fish only system at the store. Many lfs keep the fish seperated from inverts in their systems so that the fish system can be treated for parasites and so on. The ph in these systems tends to be lower than a reef system because of lack of buffering. As long as the ph is stable, and the fish was properly acclimated, however, it is perfectly safe. This is why slow acclimation of new fish is so important. You didn't say if you acclimated it or just dropped it in your tank, so this would be my first guess as to the problem.
If you did properly acclimate the fish, then my second guess is that the fish suffered a fatal reaction to being captured, handled, and dropped into a new system. Some species of fish and some individuals of otherwise hardy species can suffer fatal reactions to being captured even without suffering any kind of physical damage. These fish generally react immediately to capture by going into a kind of shuddering paralysis and then die within minutes of capture. (This is why the advice to capture saltwater fish with a clear container and not a net.)
My third guess is that the fish suffered physical damage after being released. In a new system the fish would be very nervous and easily frightened. I have lost several fish to head injuries when they slammed into the rockwork or sides of the tank. In this case, they can either die immediately or flounder around on the bottom for hours before death. A head injured fish will often breath rapidly, also.