How do you handle situations like "One of your team members has not performed on the agreed tasks"?

This is a common situation. Handling the situation depends on the importance and urgency of the job in question. Depending on the urgency of the job, it is always advisable to have a backup team or back up plan which should be activated in a situation like this. 

You have to find out the reason for such non performance and then the person responsible should be handled accordingly.

In this situation I, would first ask for the reason why the date was slipped for that particular job. If it is a genuine one I will advice him to give a prior notice of such situation in future and inorder to gey it completed as earlier possible will analyse the constraint and take necessary action like involving more than one person to complete the task, provide my/others advice based on the expertise needed.

If it is not a genuine reason will explain him about the negative impact it creates on his profile and give him some time to correct himself.