I tried running the script command manually, from a command line, and I could see the file was almost immediately uploaded 100% (it is only 34k), then there was a pause, then I got the message "Host is not communicating for more than 15 seconds", and then ultimately the session would reset and it would attempt the upload again.
I've spoken to the people at the remote site, and they tell me that each time we are uploading the entire file.
So why can't WinSCP see that? Is there some obscure bug in the remote site that we need to compensate for?
Not sure if this is useful or not, but I've been told that the remote site uses the services of Globalscape.