Can you limit the number of posts?

Yes you can, in that case you would need some code to do so. There’s example here, take a look at Disabling posting capability section

Based on your link, I modified the code to set time frame as below, but it is not working. Could you please look into it? Thanks in advance

/**
 * Check if the current user can post
 *
 * @return bool
 */
function wpufe_can_post() {
	global $post_type;
    global $wpdb;
	global $userdata;
    $user = wp_get_current_user();

	if( $post_type === 'post' ) {
		$today = date( 'Y-m-d 00:00:00', ( gmmktime() ));
		$news_count = $wpdb->get_var( "SELECT count(*) FROM $wpdb->posts WHERE post_status = 'publish' AND post_type = 'post' AND post_author = $userdata->ID AND post_modified > '$today'" );
		if( $news_count >= 1 ) {
		return false;
		}
		return true;
	}

}

/**
 * Show the message if can't post
 *
 * @param string info message
 * @return string info message
 */
function wpufe_show_message( $info ) {
    if( !wpufe_can_post() ) {
        $info = 'Sorry, you have exceeded the limit of post per day';
    }

    return $info;
}
add_filter( 'wpuf_addpost_notice', 'wpufe_show_message' );