Exchange 2013 has a feature called “Managed Availability”, it is a built-in monitoring system in Exchange.

A quick overview as per the Technet site regarding Managed Availability:

Managed availability, also known as Active Monitoring or Local Active Monitoring, is the integration of built-in monitoring and recovery actions with the Exchange high availability platform. It’s designed to detect and recover from problems as soon as they occur and are discovered by the system. Unlike previous external monitoring solutions and techniques for Exchange, managed availability doesn’t try to identify or communicate the root cause of an issue

Let’s say you need to re-create the health mailbox, here are the steps to do so:

Launch the Exchange Management shell.

Run the following command to get a list of health mailboxes:

• Get-Mailbox -Monitoring

As shown above we can see the list of Health Mailboxes, in this case we looking at MBX02 which is the 2013 Server.

The next step is to open up Active Directory Users and Computers (Ensure that Advanced Features is selected under the View Menu) and expand “Microsoft Exchange System Objects”.

Click on the Monitoring mailboxes Folder. To the right you will see all the Health Mailboxes.

As I have Exchange 2016 as well I have a number of the Health Mailboxes. In your environment you might only have Exchange 2013, highlight them all and delete them.

Now restart the Exchange Health Manager Service, this will then re-create the Health Mailboxes.

Hope it helps.