Wikimedia Bugzilla is closed!

After searching through the bugs, there should be a text field for 
immediately conducting another search with the domain-restrictions of 
the previous search, rather than requiring one to click "edit search" 
and load the search page again. [to change the restrictions on the 
search, one would still have to follow that link].  

This is perhaps an easier fix than a previous request for a more 
general solution (having a search box in the sidebar).