I just tried to create one of these and all it does is bring me back to the empty Advanced Search page when I click on the search I created.
Update: The problem occurs when you try to save the search from the search page itself. Apparently, if you RUN the search that option of saving it appears again. When you save it this time, then run it, it brings you NOT to the search results, which I would have expected, but the search page filled in with your choices. Then you have to run it.
Seems like the one option of saving it from the search page shouldn't exist if it doesn't work and the second option ought to save it, but run the search, not just fill in the fields for you.