I believe the session time variable may have been deprecated in recent EE updates, since it is no longer listed in the EE knowledge base for config variables:
$config['cp_session_ttl'] = 'insert number value here';
Default is/was 3600 seconds for that value.
Have you tried as an alternative setting the cp_session_type variable in your config.php:
$config['cp_session_type'] = 'c';
When set to cookies only (value of c), rather than using sessions (s or cs for sessions + cookies), you should then see an option on the cpanel screen next time you login to 'Auto login on future visits?'
the login will remain valid for up to 2 weeks I believe, so even on closing the CPanel, navigating back to the page later should log back in automagically.
Not a direct answer I know, but hope it helps.