Multiple command prompts with one SSH connection

Try Bitvise Tunnelier - it works for me. I set it to establish SSH tunnels while only being visible as a tray icon. It establishes the SSH connection on startup and re-establishes it as soon as connectivity is restored after a cut or after the system went to sleep. I still prefer the looks of the Putty console, so I keep using it - but for keeping tunnels up I now use Tunnelier. The only major downside I have found is the lack of IPv6 support, which Putty provides with no user action needed.

I don't believe that leaving the connection open is any more of a risk than having SSH available in the first place.

If anything, one might argue that repeated connections represented more of a risk. But that is highly theoretical based on possible sniffing of the connection attempts over the network.

The more realistic main risk from leaving the connection open is the possibility that the client PC might be compromised whilst the connection is open. So it would be sensible to set the timeout to a reasonable period such as 4, 8 or 12 hours depending on the usage patterns and the sensitivity of the data on the host system.

4 hours allows for a normal 1/2 day's work. 8 hours a nominal days work and 12 hours for a more realistic elapsed day's work. On a remote connection service that I'm currently helping to specify, I've just asked for remote connections to be kept open for 12 rather than 8 hours in order to match a more normal working elapsed day. I really don't see this as much of an increased risk since the client PC's auto-lock after 5 minutes of inactivity and there is a standing instruction to manually lock the PC when moving away from the desk.