A few months back I encountered this issue which was stopping the backup exec beremote.exe process which is required to backup Virtual Machines.
Insufficient winsock resources available to complete socket connection initiation
In my case it was a recent Windows Update that caused hundreds of false sockets to be opened within Windows Server. This was happening because the update was conflicting with the iSCSI initiator service.
Check your iSCSI initiators and if you have any that are “reconnecting”, they will need to be removed. Delete them and reboot the server.
This has happened on two Windows Server 2012 R2 instances running Backup Exec 15 and 16. On both cases, this solution resolved the issue.