Not necessarily

The question is whether such sick days are allowed by the labor contract.

It also depends on whether it is an at-will or fixed-term contract. If it is an at-will contract, usually the employer may fire the employee for no reason or bad reason. And he can certainly fire the employee if the employee is sick a lot.

If it is a fixed-term contract, the employer probably cannot fire the employee that freely.

In any case, an employer can always fire an employee. THe question is that of damages.