Without seeing the actual PHP code (that would be helpful here), I'd suggest renaming the form itself so that it is not called search just like the text box for the search.
Then, look at your code on the results page to see where you use the $search variable. You are no longer sending that variable through when you click the link (>>1 2). You are only sending offset through.
Try rewriting the links to send through like this result.php?offset=<?php stuff to come up with offset?>&search=<?php echo $search ?>.
That way you will keep sending the search variable through to the other pages that was passed in by the initial form.
Hope that helps.
Ari