You need to save your searches by clicking on the 'Save Search' button which is just above the format box to the right of the search results. Then click on the “+” to add to your saved searches. You can always go back & remove any searches you don’t want saved after all. The saved search list should stay as you left it for as long as you have an active account.
To see your saved searched click the "My Saved Searches" tab at the bottom of the page.