The link below is for NYC income based housing.
Any site thats tax credit has to comply and are monitered by the government/state.
When your renewal comes up, thats when you'll need to provide proof that you are still within their criteria for reduced housing in order to remain, but I can't tell you anything about your particular site and how closely they're monitored(by state/gov) if at all, you could also be asked to pay full market value, its difficult to give you an answer. You might want to contact them and ask that question.
NYC Affordable Housing Resource Center