I had two colonies of Zoas go in my tank the same way (except they were growing like mad on one side, and dying on the other) and it took me months to find the culprit: asterina stars. A LOT of things love to eat Zoas - dozens of types of fish, zoanthid spiders, zoanthid eating nudibranchs, asterina starfish, and various types of sicknesses they can get like zoa pox and other types of skirt diseases...
You need to get a red-flashlight and watch your zoas every night for about a half hour every day until you find out what is killing them. Also - you should be spending abotu the same amount of time during the day in case they are eating it in broad daylight.
Edit: If you don't have a red-flashlight you can use a camera flash. With all the lights out snap some flash pictures of the colony close up every minute or two and the instant lighting will not scare the predator away. That's how I caught the asterinas red handed. Every time I broke out the flashlight they hid. However, I was able to use my DSLR and Strobe Light to catch them in the act. You will want to get a "Rubber Hood" for your camera so when the flash goes off, it doesn't cause reflections off the glass. They are super cheap. External flashes work even better since you can point them from the top down and shoot through the side of the tank.
Here is a picture of my zoas in the pitch black - you can't see the stars in this picture though you can see the receding receding. This was taken using the camera method I described above and looks similar to the damage to yours:
