this is it:
// we received post data
if( qa_post_text('request') ) { ... }
PS: In your custom form you need to define 'request', e.g.
$qa_content['form']=array(
'tags' => 'METHOD="POST" ACTION="'.qa_self_html().'"',
'style' => 'wide',
'ok' => qa_post_text('okthen') ? 'Submit successful! Value is: '.qa_post_text('request') : null,
'fields' => array(
'request' => array(
'id' => 'month_dropdown',
'label' => "choose stuff:",
'tags' => 'NAME="request"',
'type' => 'select',
'options' => $dropdown_options,
'value' => '2012-05-01', // qa_html($request),
//'error' => qa_html('Another error'),
),
),