Thanks for your post.

This request is being tracked already:
Issue 2360 – Optionally do not show error message when connection is lost while idle
You can vote for it there.

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PuTTY issues:
When a device is disconnected, PuTTY is disconnected and shows the popup of disconnection, instead show a disconnection text on the title and disable typing.
Also when the device is connected back, let it get auto re-connect, instead of letting users close and re-open another session.

WinSCP screen block issue:
When I have 2 sessions (which are sessions to 2 different devices), if one disconnects, it shows the popup or reconnecting, but do we really need it? because this blocks access to the other session which is active.
There should be another mechanism to keep reconnecting to the inactive device without blocking the screen for other active sessions.