I do not understand how can that prevent the synchronization from ending. WinSCP will retrieve a list of files that exist at the moment the synchronization started. And it will synchronize only those files. If you want us to investigate further, please attach a full session log file showing the problem (using the latest version of WinSCP).
To generate the session log file, use
/log=C:\path\to\winscp.log command-line argument
. Submit the log with your post as an attachment. Note that passwords and passphrases not stored in the log. You may want to remove other data you consider sensitive though, such as host names, IP addresses, account names or file names (unless they are relevant to the problem). If you do not want to post the log publicly, you can mark the attachment as private.