There are several permissions at play here:
1. In Metadata, the permission on the flow/jobs which is inherited from the folder where they are stored.
2. The scheduled task in Windows, which is controlled by host permission in Task Scheduler.
3. File system permission on the job's source path (where it was deployed from) and deployment path (where it was deployed to/is running from)
It is unclear which permission(s) the user in question does not have.
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Greg Wootton | Principal Systems Technical Support Engineer