What are the conditions under which same day or 1 day visa processing is granted?

I am forced to apply for my entry permit the day before my flight leaves for China due to documents arriving later than expected. Will that be an acceptable reason to allow rush service? I don't want to show up to the consulate and be denied the rush processing. Then I will have to pay a lot of money to change my flight. It's for a Z type, by the way. Thanks!