Should I leave food out all day for a picky cat?

Usually not. Leaving food out all day (free-feeding) means your cat is never genuinely hungry at any single moment, which makes her less interested in any particular meal, especially wet food that goes stale fast. Most cats do better on two or three scheduled meals, each picked up after 20 to 30 minutes. The exceptions are a kitten under six months, who should have regular access to food, and any cat your vet has put on free-feed for medical reasons.

Source: Cornell Feline Health Center, “How Often Should You Feed Your Cat?”