Remember Search value between tabs

Because there are so many different search options, I'm not always sure which one is going to contain what I'm looking for. It would be great if the value I enter in the search box does not get wiped out when I go to another tab in the same general menu. Right now, the search box remembers the last thing that was entered under that tab, but that is not really useful. The most useful search is the one I'm looking for right now.