Solution 1 :
Add the Backup Exec Service Account (BESA) to the Hyper-V Cluster and Cluster Nodes.
Open Hyper V Cluster Manager. Go to properties of Cluster Name (FIGURE 2) :
(FIGURE 2)

Add the Backup Exec Service Account (BESA) account with full rights in the Cluster manager for the Hyper-V Cluster Resource/Name (FIGURE 3).
(FIGURE 3)

Note: Additionally add the BESA account to the Local Administrator group on all nodes of the Hyper-V cluster.
Restart the Backup Exec remote agent service on all Hyper-V cluster nodes.
Solution 2 :
Another cause is if there is an issue with the WMI namespace in the Hyper-V hosts. In this case , a reboot the Hyper V host(s) may be necessary. Virual Machines will need to be moved to other cluster nodes to reboot each Hyper-V cluster node one at a time.
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[ Note : This is taken in consideration that Hyper V Cluster and its configurations are configured properly. ]
Applies To
Clustered or Highly Available Virtual Machines on CSV (Clustered Shared Volumes)
Two, Three, Four Node Hyper-V Clusters
In the Example above the 3 virtual machines missing are owned by NODE1 of the Hyper-V cluster. The 3 Virtual machines available for selection are owned by NODE1 and this is the same node the Hyper-V Cluster resource is currently owned by. Live Migrating a missing Virtual Machine to the Hyper-V node where the Virtual Machine are showing up in the Backup Exec selection list will allow the Virtual machine to appear in the selection list although not desired for Load balancing and fault tolerance of the Hyper-V cluster and Virtual machine.