The ESXi Shell supports a timeout for ESXi Shell availability and a timeout for idle ESXi Shell sessions.

Availability timeout - The availability timeout setting is the amount of time that can elapse before you must log in after the ESXi Shell is enabled. After the timeout period, the service is disabled and users are not allowed to log in.

Idle timeout - If a user enables the ESXi Shell on a host, but forgets to log out of the session, the idle session remains connected indefinitely.

You can set both timeout values from the Direct Console User Interface or from the vSphere Web Client. See the vSphere Security document for detailed instructions.