You may need to force close your browser to log out of TurboTax.
If you are a Windows user, press Ctrl-Alt-Delete to open the Task Manager. Then select your browser and click on End Task.
For Mac users, click on the Apple icon and select Force Quit, then select your browser (which will probably say Not responding) and click Force Quit.
When you reopen TurboTax, check to make sure that any changes you made just before the browser froze were saved.