No seu .ssh / config no seu cliente, tente adicionar algo assim.
Host *
ServerAliveInterval 60
man ssh_config
ServerAliveInterval
Sets a timeout interval in seconds after which if no data has
been received from the server, ssh(1) will send a message through
the encrypted channel to request a response from the server. The
default is 0, indicating that these messages will not be sent to
the server...
Do putty, você deseja ajustar o Connection\Seconds between keepalives
para um valor diferente de zero.