Hi Sheldon - This starfish is very often sold in LFS's - BUT, 90% of them do die, unfortunately. I have had a few of these, with varying levels of success. As SeanK says - these starfish do a LOT better in aquariums that have a LOT of detritus lying in the aquarium. So - not really good to keep them in a coral tank....
You should try and place a small piece of fish very close to the starfish, or perhaps pink shrimp - and see if the starfish eats it. If it doesn't, then this starfish is on it's way out, unfortunately.
If it DOES eat - then you should target feed this starfish until it is healthy enough to move a lot faster through the aquarium.