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A Pivot Transformation was intermittently reporting this error code as:
The ProcessInput method on component "Pivot" (1234) failed with error code 0xC0202031. The identified component returned an error from the ProcessInput method. The error is specific to the component, but the error is fatal and will cause the Data Flow task to stop running.
Removing spaces from the "Pivot key value column name" property (and also from all downstream references to that column) appears to have avoided this error.