The ssh "timed out waiting for input: auto-logout" messages is generated by ssh upon reaching a auto-logout after an inactivity time specified by the TMOUT environment variable. If this variable is not set your session will not be auto-logged out due to inactivity. If the environment variable is set, your session will be automatically closed/logged out after the amount of seconds specified by the TMOUT variable.
To see if your auto-logout variable is set and/or see what it is set to issue the following command:
$ echo $TMOUT
Often this value is defined in /etc/profile (globally) or your user's profile (~/.profile or ~/.bash_profile).
To alter the auto-logout amount, set the TMOUT environment variable accordingly:
* TMOUT=600 #set an auto-logout timeout for 10 minutes
* TMOUT=1200 #set an auto-logout timeout for 20 minutes
* TMOUT= #turn off auto-logout (user session will not auto-logout due to session inactivity)
This value can be set globally (e.g. TMOUT=1200) in the /etc/profile file; however, each user can override the value by setting the TMOUT variable in their personal profile file (~/.profile or ~/.bash_profile). To do this simply set the TMOUT variable as you like in your profile file.
Dont forget to source the file you changed to get the settings to take effect immediately or log out and log back in.