I'm not seeing any errors or warnings in the WinSCP client GUI during these transfers. This issue was discovered later when our site threw an exception. I've since enabled WinSCP logging. I don't see anything in the log file that stands out, but I'm unfamiliar with these log files.
What sort of validation does WinSCP perform to make sure files are being transferred accurately?
I will try having a colleague replicate the problem with their machine and a different FTP client. If they have the same problem, then I presume the problem is with the vendor's FTP server that they have set up just for us.