Advance Search form $form is not the same when invoked a second time?
As I understood from your question you need to add additional style when no results found.

The file search-block-form.tpl.php in search module folder is responsible about displaying the form you could copy it to your theme folder and alter the markup as you need (You have to clear cache in order to flush theme registry).

Also take a look at the two files search-result.tpl.php and search-results.tpl.php the same could be done depending on your needs and use case.

For more clarification about theme suggestions read