I've done several tests just now and everything works as expected (I admit that I've never tried it before).
Maybe there are some specific circumstances in your case. What version of Windows are you using? Does console window for the .cmd script shows up? It someone logged to the machine when script is running? Does it run under the same user as the one logged in?
I was using one login to log in to the Windows session, but the task was running under the permissions of a different login (e.g., not mine, one whose password doesn't expire every 60 days). My login had access to the stored session information I was calling, but the other login did not. As soon as I ran WinSCP under the other login and created a stored session with the same name, everything ran fine.
Thanks for the pointer.