Can an employer who has offered you full time with benefits decide to withhold your benefits after you start working full time for three months?

I work for YAI as a DSP in Brooklyn, NY. The organization offers benefits including healthcare to full time employees. As a part time employee since Nov. 2017 I was told I would receive benefits once I start my full time schedule. Within a week a going full time in July 2018, I asked my supervisor how I can sign up for my benefits. It was then that she decided to tell me that since I made a mistake at the beginning of the month, I would not be getting benefits for 3 more months. I was written up for the first time for accidently missing an extra shift I had volunteered for with no call/no show. I was already working full time and continue to do so each week but I never heard of an organization withholding benefits for 3 months for making a mistake and being written up one time. Is that legal since I am working full time?