I believe the server will still have a default session timeout (probably 20 mins), so removing the global.asa file won't solve this.
With the second part of your question, it all really depends on how your menus are written. It's most likely they are done using layers (or Div's). If this is the case you can control if they are visable by setting element.style.display = 'block' or 'none'; This will cause it to be displayed, but before you do this you will need to have a record of whether the menu was open or closed. This would usually be stored in a cookie (although there is no reason why you couldn't do it in a session variable).
So in short the info on whether the menu is open or closed has to be written (in the case of a cookie) every time the menu is accessed, and then checked every time the page is loaded.