If there is an employee who seems to cause problems for those around them, they must be dealt with. This is when the coaching and counseling skills of a good manager come to bear. If the employee simply can't change, the company is usually better off without that employee. If nothing is done, the message that gets sent to employees is that one problem employee is going to be put ahead of the welfare and morale of all other employees. This is a very damaging message to send.
Morale is something that needs to be managed.
Carefully evaluate your management style. Is it facilitating in nature or is it dictatorial or overly assertive and direct. Encourage employees to come forward with problems, suggestions and issues. Listen carefully and acknowledge their concerns. Follow up on them and communicate results of your findings back to them.