Welcome to the Boards!
Falling apart within the first several weeks is very common with acclimation stress. How did you acclimate? Starfish usually need very long acclimations. I usually try to do a six hour acclimation with starfish if possible. They also need good water quality in a mature tank (at least six months old recommended).
There probably isn't too much you can do at this point. If only the legs fall off but the central disc stays intact, the sea star may recover.