In file lib/the-events-calendar.class.php line 2385 the code is calling:
$term_link = get_term_link( (int) $term, self::TAXONOMY );
When the value passed in for the $term is a string (a slug in this case). The method is called from public/template-tags/month.php line 2385 in the tribe_get_next_month_link().
The (int) is unnecessary and causing a wp_error to be returned since a term slug is passed to it. This breaks paging in month view when a category has been selected (and causes the next/prev month links to not render in the same category).
Let me know if you need more information, I’m using the calendar on a client’s intranet site and can’t make it available, but you can see it happening on your demo site. Go to http://wpshindig.com/events/category/wordpress-meetups/month/ (month view for the wordpress-meetups category). Hit next month, which will properly load the next month for the category, but the new next months are rendered as root links and clicking next month again will not filter by category anymore.