I've got several Sun Corals and as mentioned if they don't open they definitely won't eat. Each time I've added a new one I've always found it to be a bit of work to get them opening regularly. After a few good feedings they'll start to open up whenever they smell food in the tank. In the wild they spend their lives in caves and other low light areas. In the aquarium they tend to become nocturnal feeders so they will open up at night on their own usually, but with a little coaxing you can get them to open up and stay open during the day. Mine really get excited over Cyclop-Eeze in the water but when it comes to actually eating they much prefer the frozen mysis.
One trick that's useful when they won't open for a long time is to create a dome using the top of a plastic soda bottle, this way you can put the dome over them, put food in the dome and put the cap on. This keeps the crabs and fish out allowing the food to stay near them for a long time. If they're hungry they'll open up.