You’re absolutely going to lose weight at 500-1000 kcal a day. It’s not particularly healthy, and you’re going to lose significant muscle mass, but you will absolutely lose weight rapidly. A significant caloric deficit will not prevent weight loss; its thermodynamics. You’ll lose muscle with that much of a deficit, which in turn decreases basal metabolic rate, but you’re not going to violate thermodynamics.
How are you tracking intake? If you’re not losing weight, I don’t believe you’re tracking calories correctly. Are you using a scale and weighing portions, or just eyeballing it?