Integration services have different roles. You can check that via Hyper-V manager by opening VM settings. If this VM was backed up properly last night, then please open a support case and let our technical team investigate the issue.
4c7 wrote:I might try adding the same host as standalone later, but this doesn't make sense at all.
Not exactly. If VM is backed up successfully via standalone connection, then it must be something with VMM server and troubleshooting steps should be focused on this component.