I would say have a look at how heavy the workload is going to be over the period he's asking to have off, and if you could cope 1 man down, then let him have the time off. As a manager your responsibility is both to your staff and to the needs of the business. If you can't bend for him this once then why would he bother bending for you in the future? Even if there are jobs that need doing, could some be postponed? We all have lives outside of work...