What happens if you alter your code to this:
$groups = acf_get_field_groups();
echo '<pre>'; print_r($groups); echo '</pre>';
save_fields('group_559a17278c508', 123, array(
'tagline' => 'Test Tagline',
'other_field_name' => 'Other Value'
));
Do you see any field groups? If you do are group_559a17278c508
listed?