If the connections are over SSH you can set these settings on the SSHD's side in the config file
ClientAliveInterval 30 ClientAliveCountMax 5
Where these settings have the effect:
ClientAliveInterval: Sets a timeout interval in seconds (30) after which if no data has been received from the client, sshd will send a message through the encrypted channel to request a response from the client. The default is 0, indicating that these messages will not be sent to the client. This option applies to protocol version 2 only.
ClientAliveCountMax: Sets the number of client alive messages (5) which may be sent without sshd receiving any messages back from the client. If this threshold is reached while client alive messages are being sent, sshd will disconnect the client, terminating the session.
To get 10 minutes you'll need to adjust the times accordingly, perhaps like this:
ClientAliveInterval 120 ClientAliveCountMax 5