If you perform a search and then click on the search icon or use the keyboard shortcut, the cursor will be placed at the end of the previous search term. To search for a new term, you must highlight the existing text via mousing, Crtl-A or Shift Arrows keys and then start typing.
The majority of the time I’m using searching, I’m attempting to search for something completely different than what I searched for earlier. If I want to refine, I enter the search results page and then refine the existing term from there.
In Google’s inbox, when focus is returned to search box, the entire existing term is auto highlighted:
That allows you to start typing immediately if you have a new term to search for, or hit the right arrow key if you need to refine an existing term. As a heavy searcher, I prefer the auto-highlight method and think Discourse should consider adopting it.