An unattended installation (or update) require Administrator privileges. Having Administrator privileges for an unattended update require having a Windows service installed into the system that has those privileges. That's what for example all major web browsers do (or obviously Microsoft Windows itself). Having such service running is imo huge breach into the system. While it's justifiable for something as important as web browser, I do not think it's justifiable for something like an "FTP client". So there's no built-in mechanism in WinSCP to auto-update itself. Sorry.

If you really need it, it's not that difficult to set up a Task Scheduler job with Administrator privileges that periodically downloads the WinSCP installer and runs it. Or you can even have your existing transfer task download the WinSCP. It does not even have to install it. Just extract a ZIP archive with portable version of WinSCP.
I've posted such script while ago on Super User:
Resume uploading with built-in Windows FTP client
It downloads the latest version of WinSCP .NET assembly. To make it download the Portable package, just replace Automation with Portable in $winscpArchive.

Alternatively, there are ready-made systems that do keep software up to date. I have no experience with these myself, but for example check Chocolatey. It has WinSCP package.

I see many posts about unattended install. I don't see anything about unattended update.

I run the sftp server and I use WinSCP for multiple clients. They install manually, set a few options, and never use the GUI again. WinSCP.com is run by the task scheduler for automatic uploads and downloads.

These clients are running old versions which is causing me a lot of grief. Can I get automatic unattended updates for these clients?

Donor: YES!