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Thank you for providing the details regarding the issue you are encountering with Premium eDiscovery.
Based on your description, it appears that the export process completes, but the data is not available for download. You are encountering an error message while exporting data for the requested users, and after completion, it states "no data found." Additionally, there is an indexing issue, despite the account having the necessary permissions.
Here are some steps you can consider for troubleshooting the issue:
Check Service Health - Please verify the Microsoft 365 service health dashboard to see if there are any ongoing issues with eDiscovery or related services that might be affecting your export.
Indexing Issues - If there are indexing issues, it may affect the export results. You might want to check the status of the indexing process and ensure that it is complete before attempting to export again.
Permissions - Although you mentioned that permissions are not an issue, double-check that the necessary roles are assigned to the admin account for the eDiscovery tasks. You can verify this using the eDiscovery RBAC check in the Microsoft 365 admin center.
Re-index the Data - If possible, try re-indexing the data or running the eDiscovery search again to see if that resolves the issue.
Export in Smaller Batches - Given the size of your dataset (approximately 440 GB), consider breaking it down into smaller batches for export. This can sometimes help avoid errors related to large data sizes.
For more details, please refer the following documentation which might help you in getting some valuable insights.
I hope this information helps. Please do let us know if you have any further queries.
Thank you.