Lower-Use796's journey

I have been working part-time at a medical facility in Upstate New York for about a year now. I passed my probation period in July, but my performance results have been affected by a number of medically documented absences. My doctor filed for FMLA on my behalf, but unfortunately, it was denied because I hadn't worked the required 1,250 hours with the company. Recently, I've reached a warning level of 2 out of 4 according to company policy, and after another week of medical absences, I fear I might be at level 3 or possibly facing termination altogether. I've never been written up for any behavioral issues, and my work results have consistently been satisfactory, scoring over 85% on monthly tests. My team leaders and manager have always appreciated my contributions when I'm able to work. Now, I'm concerned about my eligibility for unemployment benefits if I get fired due to these medical absences. I want to know if my situation disqualifies me from receiving unemployment or if I might have to contest a denial.