Why isn't pagination working?

showroom.php

function grv_ebay_showroom_loop() {

	$paged			= ( get_query_var( 'paged' ) ) ? absint( get_query_var( 'paged' ) ) : 1;
	$transient		= "ebay_showroom_page_".$paged;
	$expires		= 60 * 60 * 24;

	if ( !current_user_role_is( array( 'Administrator' ) ) ) {
		$ebay_showroom	= get_transient( $transient );
	}

	if ( empty( $ebay_showroom ) ) {

		$args = array(
			'posts_per_page'   => 20,
			'paged'				=> $paged,
			'orderby'          => 'title',
			'order'            => 'ASC',
			'post_type'        => 'grv_listing',
			'post_status'      => 'publish',
			'meta_query' => array(
				array(
					'key' => 'grv_listing_hide',
					'value' => 'No',
					'compare' => '=',
				),
			),
		);

		$listings = new WP_Query( $args );
		$ebay_showroom = '';

		if ( $listings->have_posts() ) {
			global $wp_query;
			while ( $listings->have_posts() ) {
				$listings->the_post();
				global $post;
				$ebay_auction_id	= get_post_meta( get_the_ID(), 'grv_listing_ebay_auction_id', true );
				$ebay_listing		= ( ! empty( $ebay_auction_id ) ) ? true : false;
				$hidden				= ( ! $ebay_listing ) ? 'hidden' : '';
				$ebay_showroom	.= '<div class="row showroom-listing '.$hidden.'">';
					$ebay_showroom	.= '<a href="'.get_bloginfo( 'url' ).'/'.$GLOBALS['name'].'/'.$post->post_name.'">';
						$ebay_showroom	.= '<div class="col-xs-12">';
							$ebay_showroom	.= '<div class="row">';
								$ebay_showroom	.= '<div class="col-xs-4 col-sm-3 col-md-2 col-lg-2 showroom-photo">';
									$thumbnail		 = get_the_post_thumbnail( get_the_ID(), 'thumbnail', array( 'class' => "img-thumbnail img-responsive" ) );
									$ebay_showroom	.= $thumbnail;
								$ebay_showroom	.= '</div>';
								$ebay_showroom	.= '<div class="col-xs-8 col-sm-9 col-md-10 col-lg-10 showroom-details">';
									$ebay_showroom	.= '<div class="row showroom-title">';
										$ebay_showroom	.= '<div class="col-xs-12">';
											$ebay_showroom	.= '<h4>'.get_the_title().'</h4>';
										$ebay_showroom	.= '</div>';
									$ebay_showroom	.= '</div>';
									$ebay_showroom	.= '<div class="row">';
										$ebay_showroom	.= '<div class="col-xs-12 col-sm-6 col-md-6 col-lg-6">';
											$ebay_showroom	.= '<div class="row">';
												$ebay_showroom	.= '<div class="col-xs-12 col-sm-6 col-md-6 col-lg-6">';
													$ebay_showroom	.= '';
												$ebay_showroom	.= '</div>';
											$ebay_showroom	.= '</div>';
										$ebay_showroom	.= '</div>';
										$ebay_showroom	.= '<div class="col-xs-12 col-sm-6 col-md-6 col-lg-6">';
											$ebay_showroom	.= '<div class="row">';
												$ebay_showroom	.= '<div class="col-xs-12">';
													$ebay_showroom	.= ( !$ebay_listing ) ? '<h4 class="pull-right">Price: Call for Price</h4>' : '<h4 class="pull-right">Price: See Auction</h4>';
												$ebay_showroom	.= '</div>';
											$ebay_showroom	.= '</div>';
										$ebay_showroom	.= '</div>';
									$ebay_showroom	.= '</div>';
								$ebay_showroom	.= '</div>';
							$ebay_showroom	.= '</div>';
						$ebay_showroom	.= '</div>';
					$ebay_showroom	.= '</a>';
				$ebay_showroom	.= '</div>';

			}
			$big = 999999999;
			$args = array(
				'base'	=> str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
				'format'	=>	'?paged=%#%',
				'current'	=> max( 1, get_query_var( 'paged' ) ),
				'total'		=> $wp_query->max_num_pages,
			);
			$ebay_showroom .= paginate_links( $args );
		}

		set_transient( $transient, $ebay_showroom, $expires );

	}

	echo $ebay_showroom;
}