First, I’d make sure I followed all applicable company rules and procedures and any laws that govern the given situation.
People should have at least one warning and a chance to improve their performance. I would counsel confidentially and give a written warning covering a specific period of time, along with clear guidelines for improvement. Then I would watch carefully and be sure to acknowledge and praise the employee for a sincere effort to remedy the situation.
However, if counseling and warning fail to produce results, I would not hesitate to terminate the employee. Firing is probably the hardest thing a manager does because you come to know your employees as people. But when someone who is notified that his or her work is below acceptable standards won’t take steps to save his or her own job, the manager must protect the company. Again, I would make sure that my actions were properly documented and that justifiable cause for termination was shown.