Unless you have a contractual agreement, you probably have an at-will employer-employee relationship. As such, you're free to make a decision as to whether to keep a person employed. Consider the nature of the work they are performing for you. If it is health/medical related or other work which could potentially cause personal injury to another (such as a driver, conductor, construction worker, etc.) you should seriously consider the consequences of your own negligence should you see danger signs but decide to ignore them. You may need to ask some tough questions and then make a decision on whether you feel this employee is reasonably fit for work.