I don't understand the issue - first you say that you "don't have to click the search button again" but then you want the form to refresh to so you CAN hit the search button again? :)
At any rate, to answer the title of your message, if I wanted a button to be clicked only one time in the session of the form, I'd use an XML secondary data source with a field called something like SearchClicked. It would be empty in the XML file. When the button is clicked, I'd set it to one, or true, or whatever. I'd disable the button if that field was equal to one, true, or whatever I'd set it to. Then, every time the form is re-opened, the field would be blank, and when the user clicks the button, the field gets set and the button is disabled.