In my experience with my dog he would go 2 days at the most without eating when he was picky.
After 2 days of going without food he decided that he was hungry enough and decided to eat the dog food I put out for him.
Your dog should eat something within 2 to 3 days at most but if the dog doesn't eat anything after 3 days then you may have to feed it something else it desires just to keep the dog from getting sick.
Either way though your dog will eventually give in and eat something before it actually starves to death.