We currently have 2 x CAS and 3 x MBX servers all running Exchange 2013. One of the Mailbox servers has the Network \ MaintenanceFailureMonitor.Network Unhealthy. What does this check and how would this be resolved?

Hi,

Is there relevant error message en application log?

Please follow below steps for further troubleshoting:
1.Run Get-HealthReport -Server "MB1" | where {$_.HealthSet -like "Network"} | FL
2.Run Get-ServerComponentstate -Identity servername

If the state is Inactive, please run below command to active relevant component:
Set-ServerComponentState <Identity> -Component component name -Requester HealthAPI -State Active

More details about Server Component States in Exchange 2013, please refer to:
http://blogs.technet.com/b/exchange/archive/2013/09/26/server-component-states-in-exchange-2013.aspx

Is there relevant error message en application log?

Please follow below steps for further troubleshoting:
1.Run Get-HealthReport -Server "MB1" | where {$_.HealthSet -like "Network"} | FL
2.Run Get-ServerComponentstate -Identity servername

I've the same issue and did the 2 steps:
1) shows the Unhealthy

...
Server                  : SERVER (MBX)
State                   : NotApplicable
HealthSet               : Network
HealthGroup             : KeyDependencies
AlertValue              : Unhealthy
LastTransitionTime      : 12.08.2015 07:24:37
MonitorCount            : 6
HaImpactingMonitorCount : 0

...

2) shows that all states are active.

The error message is:
Maintenance workitem "Network.Maintenance.Workitem" (ID: 68) has failed. Health Manager has detected it is either set to run once and failed, or has been failing consistently. Maintenance workitem failure could cause monitoring gap and should be investigated. The error message from the last result is: System.InvalidOperationException: An item with the same primary key 112 already exists in the table. Existing definition name: IntraDagPingProbe.

Could you give futher steps to fix it?

Kind regards,
Julian

I was told this was a known bug and is supposed to be resolved in CU10. I had the issue in CU7 and just installed CU9 and it remained. Its not supposed to impact anything and I'm told it has something to do with when the server names have the same first 3 letter and the last 3 characters. 

I added the following global override:

Add-GlobalMonitoringOverride -Item Monitor -Identity "Network\MaintenanceFailureMonitor.Network" -PropertyName Enabled -PropertyValue 0 -ApplyVersion "15.0.1104.5"

The override is good until the next upgrade