There's a bug somewhere in MailPress 5.3 that prevents posts from being sent in your newsletter if they contain a featured image. I'm not exactly sure why this happens, but it appears to be related to MailPress's attempt to reproduce the TwentyTen theme's evil habit of changing your site header according to a post's featured image.
Something seems to go wrong in the process; but given that you probably don't want the image in the header of your emails to change according to a post's featured image either, the simplest solution is to disable this buggy behaviour entirely. To do this, you need to edit the file mailpress/mp-includes/class/MP_theme_html_.class.php.
In the function header_image, delete or comment out these 3 lines:
// case ( $post_id && function_exists('has_post_thumbnail') && function_exists('get_post_thumbnail_id') && function_exists('wp_get_attachment_image_src') && $post_id && has_post_thumbnail( $post_id ) && ($image = wp_get_attachment_image_src( get_post_thumbnail_id( $post_id ), 'post-thumbnail')) && ($image >= self::HEADER_IMAGE_WIDTH) ) : // echo $image; // break;