Thanks for your post.

This issue is being tracked already:
https://winscp.net/tracker/1498

Can you send me an email, so I can send you back a development version of WinSCP for testing? Please include link back to this topic in your email. Also note in this topic that you have sent the email. Thanks.

After upgrade to 5.9.3 from a slightly older version, when session is disconnected, and "save password for session" is checked,
1) system requires to enter password again;
2) then offers to reconnect;
3) when reconnected, password is asked again.

Inconvenient that password is not saved, even if asked to; but even asked twice when reconnecting.