You’re getting this error message when the source or target Exchange server (or office 365) is not accessible anymore.
The connection to the source or to the target Exchange server may be throttled due to high load on the server.
If the error (ErrorMailboxStoreUnavailable, ErrorTimeoutExpired, ErrorBatchProcessingStop) happens only one time, the item falls in error and the migration continues (it’s not interrupted).
The platform supports delta passes. The next time you restart the migration, items in error will be reprocessed and migrated.
Action : For these minor errors, you have to manually restart the migration.
If the error happens too frequently during a short period, it’s probably a throttling issue and the platform automatically stops the migration and restarts later (it reschedules it 20 minutes later).