Get customers that have ordered consistently each month - Oracle SQL

I'm trying to extract customers which have placed orders each month in a given period. I'm trying to include all customers up to the point they stop placing an order. continuous

I've created the result that I'm trying to extract, in the table below.

I have an query which assigns each customer a sequential "DATE" since their first order and assigns status based on their order activity, essentially the first three columns in the above table. I'm trying to write a script to get the New Status column which would be the same as status up to the point where status = 'Stopped Order" and from that point onward, it should always be Stopped Order.

I've tried to use a recursive CTE (copied below) using LAG function, but it doesn't work. It just returns the previous status as the new status.

STOPPED_ORDER_ (CUSTOMER, DATE, STATUS, NEW_STATUS, COUNT_) AS
(
SELECT
CUSTOMER,
DATE,
STATUS,
LAG(STATUS) OVER (PARTITION BY CUSTOMER ORDER BY DATE) NEW_STATUS,
1 AS COUNT_
FROM ORDER_STATUS *-- order_status is another cte which assigns status and date *
UNION ALL
SELECT
CUSTOMER,
DATE,
CASE
  WHEN NEW_STATUS = 'STOPPED ORDER' THEN 'STOPPED ORDER' 
    ELSE STATUS END STATUS,
NEW_STATUS,
COUNT_ + 1
FROM STOPPED_ORDER_
WHERE COUNT_ < 1
)

I've tried different iterations of the following code but it doesn't work. It always returns the following result

You can achieve this by using the first_value analytic function, like so:

WITH your_results (Customer, order_date, STATUS)
  AS (SELECT 'CUST001',   DATE '2022-07-01',  'First Order' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2022-08-01',  'Continuous Order' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2022-09-01',  'Continuous Order' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2022-10-01',  'Stopped Order' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2022-11-01',  'N/A' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2022-12-01',  'N/A' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2023-01-01',  'N/A' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2023-02-01',  'N/A' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2023-03-01',  'Reactivated' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2023-04-01',  'Continuous Order' FROM DUAL UNION ALL
      SELECT 'CUST001',   DATE '2023-05-01',  'Stopped Order' FROM DUAL)
SELECT customer,
       order_date,
       status,
       NVL(first_value(CASE WHEN status = 'Stopped Order' THEN status END IGNORE NULLS) over (PARTITION BY customer order BY order_date), status) new_status
FROM   your_results;

CUSTOMER ORDER_DATE  STATUS           NEW_STATUS
-------- ----------- ---------------- ----------------
CUST001  01/07/2022  First Order      First Order
CUST001  01/08/2022  Continuous Order Continuous Order
CUST001  01/09/2022  Continuous Order Continuous Order
CUST001  01/10/2022  Stopped Order    Stopped Order
CUST001  01/11/2022  N/A              Stopped Order
CUST001  01/12/2022  N/A              Stopped Order
CUST001  01/01/2023  N/A              Stopped Order
CUST001  01/02/2023  N/A              Stopped Order
CUST001  01/03/2023  Reactivated      Stopped Order
CUST001  01/04/2023  Continuous Order Stopped Order
CUST001  01/05/2023  Stopped Order    Stopped Order

You can use MATCH_RECOGNIZE to perform row-by-row pattern matching:

SELECT customer,
       order_date,
       status,
       CASE cls
       WHEN 'AFTER_STOP' THEN 'Stopped Order'
       ELSE status
       END AS new_status
FROM   order_status
MATCH_RECOGNIZE(
  PARTITION BY customer
  ORDER BY order_date
  MEASURES
    classifier() AS cls
  ALL ROWS PER MATCH
  PATTERN ( first_order any_order* (stopped_order after_stop*)? )
  DEFINE
    first_order   AS  status = 'First Order',
    any_order     AS  status != 'Stopped Order'
                  AND ADD_MONTHS(PREV(order_date), 1) = order_date,
    stopped_order AS  status = 'Stopped Order'
                  AND ADD_MONTHS(PREV(order_date), 1) = order_date,
    after_stop    AS  ADD_MONTHS(PREV(order_date), 1) = order_date
);

Which, for the sample data:

CREATE TABLE ORDER_STATUS (Customer, order_date, STATUS) AS
SELECT 'CUST001',	DATE '2022-07-01',	'First Order' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2022-08-01',	'Continuous Order' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2022-09-01',	'Continuous Order' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2022-10-01',	'Stopped Order' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2022-11-01',	'N/A' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2022-12-01',	'N/A' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2023-01-01',	'N/A' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2023-02-01',	'N/A' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2023-03-01',	'Reactivated' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2023-04-01',	'Continuous Order' FROM DUAL UNION ALL
SELECT 'CUST001',	DATE '2023-05-01',	'Stopped Order' FROM DUAL;

Outputs:

fiddle