I ran into the same issue. Jonathan Lahijani was correct the issue is on line 211 of the plugin's index.php file. It reads
echo '<span class="post-date">'.date($format.(($instance['show_time'] == 'yes')?', '.get_option('time_format'):''), strtotime(($instance['date_to_show'] == 'publish')?$lcptu->post->post_date:$lcptu->post->post_modified)).'</span>';
It is basicly checking if the $instance['date_to_show'] is set to or equals 'publish' then show the publish date, if not so the last modified date. The issue with this line is the $instance['date_to_show'] option is never saved in the database as is it missing from the widgets function update($new_instance, $old_instance).
To fix this add the following link just below line 50 in the index.php file:
$instance['date_to_show'] = ($new_instance['date_to_show'] == 'publish')?'publish':'modified';
This will properly save the option and the the date_to_show check will have something to test.
Hope to see this in the next release. If you have any questions just post back to this thread.