I never click on that logo, there is no need to. The timeout can be a few minutes, can be 15 mins. It seems random to me. All I know is that I don't want to have to keep logging in as the admin. Let me set a timeout for users, but let me the admin stay logged on until I log off.
EDIT: @uroni can you shed some light on the web interface time-out issue? What are the defaults and where are they set?