No, there's no error message in either CMSDesk or Administration Event Log...
I think this is the error but I don't know the fix since it's really not clear in the API Documentation. Can you please correct it for me?
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DataClassInfo customTableClassInfo = DataClassInfoProvider.GetDataClass(tablename);
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CustomTableItemProvider ctiProvider = new CustomTableItemProvider(CMSContext.CurrentUser);
....
ExportProvider.ExportObject(customTableClassInfo, exportFilePath, websitePath, CMSContext.CurrentUser);