Set yo publish as default

You will be able to change post status with filter hook.
Eg: Save below php code as php file, and upload and activate it.

<?php
/*
Plugin Name: Really Simple CSV Importer Publish Immediately add-on
Version: 0.1
*/

class rscsvi_publish_immediately {
	// singleton instance
	private static $instance;

	public static function instance() {
		if ( isset( self::$instance ) )
			return self::$instance;

		self::$instance = new rscsvi_publish_immediately;
		self::$instance->run_init();
		return self::$instance;
	}

	private function __construct() {
		/** Do nothing **/
	}

	protected function run_init() {
		add_action( 'init', array( $this, 'add_filter' ) );
	}

	public function add_filter() {
		add_filter( 'really_simple_csv_importer_save_post', array( $this, 'filter_save_post'), 10, 2 );
	}

	public function filter_save_post($post, $is_update) {
		if ( ! $is_update ) {
			$post['post_status'] = 'publish';
		}
		return $post;
	}

}

$rscsvi_publish_immediately = rscsvi_publish_immediately::instance();

Several reasons can generate errors while importing. I have some questions.

1. Could you check your error message? If you got white page, you should turn debug mode on.
2. Every time stops when imported 3k posts even if you change server variables? If so, what is on line 3000 and 3001?