I tried to feed it a bitter poffin (Contests), and it said "Beautifly won't eat anymore.". It has high happiness and I don't find anything out of the ordinary. Oh and if it's important in any way it's a level 70...
Pokemon can eat only 12poffins(if I remember right)
There will be sheens below the profile of pokemon which shows its apperence(Cool, Beauty Etc). If the sheen is full, the pokemon can't eat anymore
Because when a Pokemon's sheen is full, You won't be able to feed it any more poffins. You should try feeding a poffin once a day for your Beautifly. When you don't, She/he will get her/his sheen full quickly.