When you do a search on the website for a task I think the search box should not disappear! Often you don't find exactly the task you are looking for and you need or want to directly do another search. Currently, if you do a search, it switches to a "Save search as" screen. In my view it is far more probable that someone would want to do a slightly different search than they would want to save the search they have just done. Personally, I find myself forever clicking on "Modify this search" just so that I can get back to the search box! For me doing another search is thousands of times more likely than saving an existing search.