how do I increase the ssh login timeout

Is this when you leave the session idle for a time, and you are automatically logged out? This would be a Linux configuration issue, and not AWS, which could be being enforced several ways (or could be a combination of reasons), including:

TMOUT https://www.tecmint.com/tmout-auto-logout-linux-shell-idle-sessions/

Timeout in sshd_config https://www.tecmint.com/increase-ssh-connection-timeout/

(I don't usually like linking to non-AWS sites but there's aren't any docs about this on AWS).

If your problem is something else can you give more details, including which version of Linux you are running.