Try adding <?php session_start(); ?>
to the top of the page... maybe the session isn't being set properly.
If you open your dataAssist Search server behavior do you have the "store in session" option enabled? It should keep your search filter until the trigger fires again, and with that trigger it shouldn't fire when you add a url parameter search, so the filter should be maintained.
Something must be happenning where it is not storing the filter in the session properly.