One possible reason for scheduled Data Package failed to process has to do with permission. You can verify this by tracing the target SSAS server to see if any error is generated at the time of scheduled process.
Analyzer utilize SQL Agent to schedule repeated tasks like subscription/schedule jobs and Data Package processing jobs. Here the error indicated that the 'NT SERVICE\SQLSERVERAGENT' user has no permission to process the target cube.
We can verify this SQL Agent job which indeed is set to run as SQL Agent service account
To fix this issue is to grant SQL Server Agent Service Account the privilege to process the cube, you can do so by granting it globally for all the cubes or specifically to a target as shown here by creating a new Role for the target cube database then add the 'NT SERVICE\SQLSERVERAGENT' user to the role and grant the role the power to process this database.