You probably know this so forgive me if you do, but being a witness to this personally on more than one occasion... a cat NEEDS to eat or they can get a life-threatening condition called hepatic lipidosis (fatty liver). It can develop in as little as 24 hours without eating.
If need be, there are appetite stimulants you can try from your vet, or you can "force feed" her, but a cat that isn't eating is not good.
It sounds like you're already off to a good start though with syringe feeding.
GOOD LUCK!
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