Screen options aren't saving

Same here. Not theme dependent. Not plugins dependent.
Wp-core issue, screen.php was changed, spent 2 hours to catch this issue.

Function get_hidden_columns( $screen ) was reworked from:

function get_hidden_columns( $screen ) {
	if ( is_string( $screen ) ) {
		$screen = convert_to_screen( $screen );
	}

	$hidden = get_user_option( 'manage' . $screen->id . 'columnshidden' );

	$use_defaults = ! is_array( $hidden );

	if ( $use_defaults ) {
		$hidden = array();

		/**
		 * Filter the default list of hidden columns.
		 *
		 * @since 4.4.0
		 *
		 * @param array     $hidden An array of columns hidden by default.
		 * @param WP_Screen $screen WP_Screen object of the current screen.
		 */
		$hidden = apply_filters( 'default_hidden_columns', $hidden, $screen );
	}

	/**
	 * Filter the list of hidden columns.
	 *
	 * @since 4.4.0
	 * @since 4.4.1		Added the <code>use_defaults</code> parameter.
	 *
	 * @param array     $hidden An array of hidden columns.
	 * @param WP_Screen $screen WP_Screen object of the current screen.
	 * @param bool      $use_defaults Whether to show the default columns.
	 */
	return apply_filters( 'hidden_columns', $hidden, $screen, $use_defaults );
}

to:

function get_hidden_columns( $screen ) {
	if ( is_string( $screen ) ) {
		$screen = convert_to_screen( $screen );
	}

	$hidden = get_user_option( 'manage' . $screen->id . 'columnshidden' );

	$use_defaults = ! is_array( $hidden );

	if ( $use_defaults ) {
		$hidden = array();

		/**
		 * Filter the default list of hidden columns.
		 *
		 * @since 4.4.0
		 *
		 * @param array     $hidden An array of columns hidden by default.
		 * @param WP_Screen $screen WP_Screen object of the current screen.
		 */
		$hidden = apply_filters( 'default_hidden_columns', $hidden, $screen );
	}

	/**
	 * Filter the list of hidden columns.
	 *
	 * @since 4.4.0
	 * @since 4.4.1		Added the <code>use_defaults</code> parameter.
	 *
	 * @param array     $hidden An array of hidden columns.
	 * @param WP_Screen $screen WP_Screen object of the current screen.
	 * @param bool      $use_defaults Whether to show the default columns.
	 */
	return apply_filters( 'hidden_columns', $hidden, $screen, $use_defaults );
}

Added $use_defaults.

Replacing /wp-admin/includes/screen.php with file from 4.4.0 will resolve screen options saving, but I really don’t know where we should go further.

in my case… I am running my own server, tuned by myself, with no any storage or sql issues. apache2/mpm_event + php5-fpm(5.5.9) + mysql 5.6 under ubuntu/x64 with 1tb ssd storage running 8 sites.

forget to mention, and this is important: after replacing screen.php, I’ve cleaned (.*)manageedit-postcolumnshidden, fields in usermeta tables.

by the way, looks like problem is in sql table meta key name.. there was two keys with same name, but one was with db prefix, like wp_manageedit-postcolumnshidden, another – without, just manageedit-postcolumnshidden.

and after deleting both and saving screen options, manageedit-postcolumnshidden the only which exists in db now.

I have two sites with no differences screen.php, but one site have a problem but another not.
That tells me replacing screen.php won’t help.

But problem fixed after deleting meta_key=”wp_manageedit-postcolumnshidden” and meta_key=”manageedit-postcolumnshidden” records on the table wp_usermeta.

Thanks, sexymazafaka.