When you edit a saved search a message will appear as follows:

If you click the save button you will overwrite your current search with the new details.

If you change the name of the search and click save you will create a new search using that name.

If you navigate away from Quantify without saving or close your browser the last search details you used will still be displayed next time you log in. However, if you load another search without first saving you will lose the changes you made to the unsaved search.