Thought this was an issue with Webform. However, the developer noted it was related to Views Data Export not initializing the view for each batch. Here are the errors:

Trying to get property of non-object in webform_handler_field_submission_data->render() (line 181 of /sites/all/modules/webform/views/webform_handler_field_submission_data.inc).
Trying to get property of non-object in webform_handler_field_submission_data->render() (line 184 of /sites/all/modules/webform/views/webform_handler_field_submission_data.inc).
Trying to get property of non-object in webform_handler_field_submission_data->render() (line 198 of /sites/all/modules/webform/views/webform_handler_field_submission_data.inc).
Trying to get property of non-object in webform_handler_field_submission_data->render() (line 199 of /sites/all/modules/webform/views/webform_handler_field_submission_data.inc).
Trying to get property of non-object in webform_handler_field_submission_data->render() (line 206 of /sites/all/modules/webform/views/webform_handler_field_submission_data.inc).

It only occurs when doing a batch export where the exported rows is greater than the batch segment. For example, I have batch segment set to 500. If the export is less than 500 rows, it doesn't give any errors, but if it is above 500, it gives the above error per row.