My theory is that WinSCP sends the rename operation after sending the file data, without waiting for the close operation to succeed. I implemented a workaround in the server, which delays rename operations when the file name ends with ".filepart". This does fix many cases, but since this is a timing issue, it does not work in 100% of cases. In my testing, if I wait for completion of the close operation, the rename always succeeds.
I feel that this is a bug in WinSCP. The fact that my server receives a rename operation before replying to the close operation indicates this is the case. I am happy to provide more information if necessary.