I ran into this problem with a couple of WooCommerce websites I maintain. During checkout, the field for VAT Number is not automatically filled in for logged in users, in spite of the VAT Number being present in the database.
WooCommerce support assured me this will be fixed in a next release, in the meantime, you can use this quick fix:
add_filter( 'woocommerce_checkout_fields', function( $fields ) {
$fields['billing']['billing_vat_number']['default'] = get_user_meta( get_current_user_id(), 'vat_number', true );
return $fields;
});