Where I work, they can fire you after 3 doctor notes in a rolling 6 month period. I am actually on the chopping block myself. I don't think it's ethical but it seems like companies can do whatever they want. Check your employee handbook if you have one and check if your state is an "employ at will" state. If it is, then they can fire you for just about anything. Good luck
An employer can legally fire somebody for many absences but if there is no proof that you had a medical reason. However, this will also be determined by the problems that arose from this situation. Some employers will consider terminating your services if your absence is causing more loss in the business.
Most states are "employment at will" states which means they don't even need a reason to fire you. However, if you are not fired "for cause" you can get unemployment. Whether multiple absences for illness is "cause" or not depends on the employee handbook or state law.