Just like you could in the old vSphere C# Client, users can also configure a session timeout for the new vSphere Web Client in the latest release of vSphere 5.1. This not only ensures that idle sessions automatically disconnect after a certain period of time but also helps reduce the resources consumed on the vCenter Server as each session allocates a certain amount of resources.
To configure the session timeout, you will need to login to the server running the vSphere Web Client service (which is usually your vCenter Server) and find the webclient.properties file and change the default timeout and then restart the vSphere Web Client service. For the VCSA, the default timeout value is 120 minutes and I assume it is the same default for the Windows vCenter Server.
Step 1 - Locate the webclient.properties file:
%ALLUSERPROFILE%\VMware\vSphere Web Client\webclient.properties
Step 2 - Un-comment and change session.timeout value to desired value:
session.timeout = 120
Step 3 - Restart the vSphere Web Client Service:
You will need to restart the vSphere Web Client service for the changes to go into effect. For the Windows vCenter Server, just restart the vSphere Web Client service and for the VCSA, run the above command.
In my lab, I configured the time out to be 1 minute, once the session has gone idle for the configured period, you will automatically be logged out and brought back to login page with the following message: