My theory is that Idols do not ship well. If you get a good one, then you are lucky, and you stand a chance of having it live for a long time.
That being said, here are some other theories I have. They are theories because I have observed them with my 7 1/2 year-old Moorish Idol, but they may not apply universally.
1. When young, they need to eat often. They don't eat a lot at a time, but do better when they can graze all day long. I feed 2-3 times a day, and over feed so that the pellets are laying around on the bottom. The idol will eat all day long that way. Not great for a reef tank, but works for me.
2. They are rather timid, and other more aggressive fish will out compete them. I have removed at least two fish at separate times because they were either being aggressive or just outcompeting the Idol. (Asfur Angel, French Angel)
3. Mine has occasionally gone on hunger strikes. I usually get it eating again with Rod's food or Larry's Reef frenzy.
4. Nori sheets help with streamer growth. Greens seem to be important to their diet. They will even eat byropsis, though not enough to keep it in control.
5. Mine has never eaten sponge, or if it did, it was naturally growing in my tank or it is somehow in the fish food that I have given. For those that think sponge is the answer to their dietary needs, I have not found this to be the case.
4. Their mouth is not that strong. They prefer smaller foods. Smaller pellets.
5. They "blow" at food on the bottom to make it rise up off the sand then eat it. Quite interesting to watch.
6. My experience, like others, is that the Idol eats just about anything, frozen foods, flake foods, pellet foods, and other things including zoanthids. But sometimes they stop eating too. Don't know why.
7. Over the years, I have treated my Idol for ick at least 3 times using copper, treated for flukes with Prazipro, and also used Paraguard on it for other fish being sick in the same tank. The Idol was not adversely affected by any of these medications.
Hope this helps.