According to this questions:
PuTTY - Automatic Reconnect After Internet Interruption?
"Tunnelier" is the answer, but I'm wondering if anyone could expound on why Putty/PuttyTray/WhateverPuttyMods don't keep the connection alive/restart when it drops? Or perhaps point me to a working solution that they have personal experience with?
WinSCP has no problem doing this using an SSH connection, so it's gotta be possible.