The SCOM alert for MSExchangeDelivery service is failing due to this exception:
Microsoft.Forefront.Monitoring.ActiveMonitoring.Smtp.Probes.MailboxDeliveryAvailabilityProbe+MailDeliveryAvailabilityProbeException: Multiple different exceptions
at Microsoft.Forefront.Monitoring.ActiveMonitoring.Smtp.Probes.MailboxDeliveryAvailabilityProbe.DoWork(CancellationToken cancellationToken)
at Microsoft.Office.Datacenter.WorkerTaskFramework.WorkItem.Execute(CancellationToken joinedToken)
It turns out the health mailbox was full and unable to accept new messages.
To resolve this issue I stopped the MSExchange Health Manager service and deleted all the AD accounts for Health Mailboxes. Health Mailboxes can be found in the Monitoring Mailboxes OU which is inside the Microsoft Exchange System Objects OU by default. After removing the AD objects I restarted the health manager service and new health mailboxes are created automatically.