About the states of virtual machines in Hyper-V:
A Hyper-V virtual machine can be in any of the following states: Running, Saved, Paused or Off.

About Hyper-V online and offline backups
Microsoft provides the following two types of Hyper-V virtual machine backups..

Online backup:  The VM that  is in  Running state is briefly quiesced for the backup. User access during the backup continues without interruption.
Offline backup: A virtual machine that is in the Running or Paused state is rendered temporarily inactive (Brought to a "Saved State" . It is returned to its original state before the backup completes. User access during the backup is interrupted.

How a VM in Hyper-V is designated to be backed up  either in "online" or "offline" backup mode.?
Type of backup (online or offline) is a Microsoft designation and the backup applications can not decide about how to backup a virtual machine as it depends on several conditions.
 

Conditions that determine online vs. offline backups.

A Hyper-V online backup can be performed with no downtime on a running virtual machine when all of the following conditions are met:

• The Hyper-Vintegration services are installed and the VSS integration service is enabled
• All virtual machine disks are configured within the guest operating system as NTFS-formatted basic disks. If the virtual machine uses dynamic disks or the FAT or FAT32 file system, an online backup cannot be performed. (Dynamic disks and basic disks are disk types defined by Microsoft for certain Windows operating systems)
• Each virtual machine volume must specify itself as the storage location for its shadow copies. For example, the shadow copy storage for C:\ must be configured on the C:\ volume. The shadow copy storage for D:\ must be on D:\, and so forth.
• The storage configuration of the virtual machine is not compliant.

If these conditions are not met, the backup is performed offline. An offline backup results in some downtime on the virtual machine. If the virtual machine is in the Running or Paused state, it is put in a Saved state as part of the offline backup. After the backup is completed, the virtual machine is returned to its original state.

For a complete list of conditions required for online backup, refer to Microsoft Hyper-V documentation 

Uncheck the "Exclude virtual machines that must be put in a saved state to back up " option in the Backup job properties.

If the above solution is not satisfactory, Microsoft should be contacted to identify why the virtual machines in question can not be backed up using the "Online backup mode".

Workaround (until the issue is identified)

Run a Remote Agent backup (as if you would backup a physical machine)
or
Divide the job in different jobs to group the virtual machines based on the backup mode.