Nah... still didn't work, so I duped the search results page, deleted what I don't need and expanded on what I do need and all is now good as far as retaining the expected search result. However, my second posted question about retaining the entered search text is not working entirely again!
If I move from the search results page to another and click the back button, then I get an alert asking if I want to resubmit the search box. I click OK and the searched text show as I expect it to. If I click a text link on the page, the search results are still filtered as expected, but my searched text is now missing.
Obviously, on returning to the page in anyway apart from hitting the back button means the session I created has lost it's value for some reason, but I don't know why it keeps doing it.
The pages in question are attached.