If there's no sugar, I'm assuming there are artificial sweeteners instead? In which case I suppose it would really be no different to drinking a can of diet fizzy drink? If so, you could probably have 3 servings per day as they would count for your 3-per-day artificial sweetener allowance. (This is if you're in Induction, by the way)
I would add, though, that if you don't lose weight that would be the first thing to cut out - some people don't react well to artificial sweeteners and find they can stall or slow weight loss.
Just thought I'd mention that in case you weren't aware of it.