This is probably happening because you are trying to post to Facebook from a page served on your local development environment. Facebook can’t resolve URLs that begin with localhost or any other pages that are not publicly accessible. Facebook posting should work from a petition hosted on a live public website.
Can you post a link to your petition page so I can have a look?
Ok, it looks like the URL of your site isn’t being sent to Facebook because the hidden form element that holds that URL isn’t being completed. This may be because you have a single page website that doesn’t make use of the WordPress post loop.
You can fix the problem manually and then I’ll see if I can find a solution for these types of sites for a future update of the plugin.
To fix the issue, go into the plugin’s folder and open the file, includes/widget.php. Then look for lines 176 and 177:
<input type="hidden" id="dk-speakup-widget-permalink-' . $petition->id . '" value="' . get_permalink() .'" />
<input type="hidden" id="dk-speakup-posttitle-' . $petition->id . '" value="' . esc_attr( urlencode( get_the_title() ) ) .'" />
Change these lines to the following:
<input type="hidden" id="dk-speakup-widget-permalink-' . $petition->id . '" value="http://www.wesupportfeni.com/" />
<input type="hidden" id="dk-speakup-posttitle-' . $petition->id . '" value="We+Support+Feni" />
That should get the Facebook submissions working.