I know this is pretty old, but I found this thread when I was searching for an answer to the same problem. Fortunately, I was able to solve the issue and I thought I'd share.
All I had to do was close my browser completely, stop the development server (right click on the task bar and select "stop") and then rerun the Admin tool. I was using firefox as my default browser and I had left it open all night. Even though I had closed the project, I guess the session cookie was still in the cache and wouldn't allow me to use the tool. In fact, I was only getting the timeout message after I selected the development server and picked "Open in Web Browser" - it didn't do it automatically when it was timed out.
I'm sure badjuju has either figured this out or moved on, but for anyone else who might have the same issue - hope this helps!