Hi supamarine.
Usually problems due to what and how much is being eaten is the opposite as to what you have said. Clownfishes get 'floating bloat' problem if you give them too much floating pellets. Excessive floating flakes can also lead to 'floating bloat', but in rare circumstances.
I feed my clownfishes all the time, sometimes to the point where they will not eat. They never have problems. Healthy clownfish, however, will go to food even after just being fed, and at least gulp and spit it out (if they are full).
The only thing that 'may' be worth noting is that the clownfish may have swallowed a piece too big and have a hard time to swallow it. However, I see this happening just right after it enters the mouth of the clown. For a couple seconds the fish will shake left and right in an attempt to bring it down to their stomach. Choking usually causes death almost instantaneously, which isnt' the case with your clownfish.
With your clownfish, I would look somewhere else besides food. Other fish in the tank? Any new inhabitants recently added? Any tank water not from your tank added recently? Rapid breathing and laying down in sand/bottom of tank are clues to more problematic clownfish diseases, like brooklynella or amyloodinium.
Keep us posted.
- Elmo