I would like to suggest that either (a) one can pin a search range which will remain default until changed to something else or (b) that the last used search range "sticks" until changed.
When one is studying a particular section of Scripture or resource(s), the same range is searched over and over. Unfortunately, although one can save a range, it does not stick when one closes the search window or invokes the search from the context menu. It would be nice to be able to retain settings until changed to something else.
Pinning would probably be a better solution than "sticking" because it gives choice to the user. Some users could be annoyed by a sticking behaviour.