Even when my Bella was pretty little, she'd sometimes go 12 or more hours without eating. I'd coax her, but she ate when she was ready. I've since learned that lack of appetite CAN be a sign of liver diease which is VERY common in Yorkies (31 times more likely than any other breed). Now that I feed her homecooked food that is much lower in protein, she eats more often easily! She still sometimes snubbs food or sometimes doesn't eat everything I give her, but she eats VERY consistently now, even when she'd rather eat what's on my plate than hers
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Just something to think about.....since he will be at the vet, have you thought about getting some bloodwork done? I know he's a Yorkie mix, but I'd think the possibility was still there, and it's a good idea to have all Yorkie's tested for liver disease. (The best test for it is called a Bile Acid Test, but it won't be able to be done on the same day as the neuter because it is a 2 part test that requires eating between.)