Let visitors page through all months (not just the populated date range)

continual month pagination.php

/**
 * Allows visitors to page forward/backwards in any direction within month view
 * an "infinite" number of times (ie, outwith the populated range of months).
 */
class ContinualMonthViewPagination {
	protected $tec;

	public function __construct() {
		add_filter( 'tribe_events_the_next_month_link',     array( $this, 'next_month' ) );
		add_filter( 'tribe_events_the_previous_month_link', array( $this, 'previous_month' ) );
	}

	public function next_month() {
		$url = tribe_get_next_month_link();
		$text = tribe_get_next_month_text();
		$date = $this->tec()->nextMonth( tribe_get_month_view_date() );
		return '<a data-month="' . $date . '" href="' . $url . '" rel="next">' . $text . ' <span>&raquo;</span></a>';
	}

	public function previous_month() {
		$url = tribe_get_previous_month_link();
		$text = tribe_get_previous_month_text();
		$date = $this->tec()->previousMonth( tribe_get_month_view_date() );
		return '<a data-month="' . $date . '" href="' . $url . '" rel="prev"><span>&laquo;</span> ' . $text . ' </a>';
	}

	/**
	 * Can be simplified in future, but for the moment means this snippet
	 * should work with 3.10+ as well as older versions of TEC.
	 * 
	 * @return Tribe__Events__Events
	 */
	protected function tec() {
		if ( ! isset( $this->tec ) ) {
			if ( class_exists( 'Tribe__Events__Events' ) ) $this->tec = Tribe__Events__Events::instance();
			elseif ( class_exists( 'TribeEvents' ) )       $this->tec = TribeEvents::instance();
		}

		return $this->tec;
	}
}

new ContinualMonthViewPagination;