I have added this issue to the tracker:
Bug 2126 – Moving WebDAV transfer to background aborts the transfer if the server commits the interrupted foreground transfer

I've just sent you an email, with the subject "Questioner from WinSCP forum".

Yes, I'd like you to do some testing. So can you email me on my address (check my forum profile).

Thanks for your reply. Unfortunately the email I used to register was only a temporary one. Assuming the debug version has a fix for my issue, I'll just wait until the next official release, as it's not really a big deal. If you wanted me to do any testing, would it be possible to attach the debug version as a private file? If not, apologies for the inconvenience.

Thanks for the log.
I have sent you an email with a debug version of WinSCP to the address you have used to register on this forum.

martin wrote:

Can you post a session log file for your other problem?

Here's the log file. Sorry it took me a while to gather.

Yes, it shows as "Completed", meaning that the transfer is no longer in process. I understand it might be confusing, but it's not a bug as such.

Can you post a session log file for your other problem?

This bug occurs when connecting via WebDAV (haven't tried any other protocols) on the latest version of WinSCP. Knowing my internet connection is not the greatest, I decided to test what would happen if the transfer fails, by starting a transfer and then stopping the WebDAV server on my phone. Initially, I get the popups saying the transfer failed, but it's shown as completed in the queue. On a side note, but still somewhat related – pressing process in background immediately adds the transfer to the queue and shows it as completed, regardless of the actual progression.