지금.. CTE가 되는 DBMS를 가지고 있지 않아서 돌려보진 못했는데, 이런 식으로 풀 수 있을 것 같네요.
(MS-SQL 에서는 RECURSIVE 키워드를 뺍니다.)

WITH RECURSIVE C AS (
    SELECT ID, REG_UYEAR
    FROM tbl_name
    WHERE REG_UYEAR = 2019
    UNION ALL
    SELECT T.ID, T.REG_UYEAR
    FROM C
        INNER JOIN tbl_name T ON T.ID = C.ID AND T.REG_UYEAR = (C.REG_UYEAR - 1)
)
SELECT ID, COUNT(*)
FROM C
GROUP BY ID;

단, DDD 회원이 0회인건 안나올텐데, 꼭 필요한거면 LEFT OUTER JOIN을 적절히 추가하시면 됩니다.

WITH t AS
(
SELECT 1 seq, 'AAA' id, 2017 reg_uyear
UNION ALL SELECT  2, 'AAA', 2018
UNION ALL SELECT  3, 'AAA', 2019
UNION ALL SELECT  4, 'BBB', 2017
UNION ALL SELECT  5, 'BBB', 2019
UNION ALL SELECT  6, 'CCC', 2018
UNION ALL SELECT  7, 'CCC', 2019
UNION ALL SELECT  8, 'DDD', 2018
UNION ALL SELECT  9, 'EEE', 2019
UNION ALL SELECT 10, 'FFF', 2019
UNION ALL SELECT 11, 'GGG', 2019
)
-- 1. Row_number 를 이용하여 조건 주기
SELECT id
     , COUNT(CASE WHEN x = 2019 THEN 1 END) cnt
  FROM (SELECT id
             , reg_uyear + ROW_NUMBER() OVER(PARTITION BY id ORDER BY reg_uyear DESC) - 1 x
          FROM t
         WHERE reg_uyear <= 2019
        ) a
 GROUP BY id
;

WITH t AS
(
SELECT 1 seq, 'AAA' id, 2017 reg_uyear
UNION ALL SELECT  2, 'AAA', 2018
UNION ALL SELECT  3, 'AAA', 2019
UNION ALL SELECT  4, 'BBB', 2017
UNION ALL SELECT  5, 'BBB', 2019
UNION ALL SELECT  6, 'CCC', 2018
UNION ALL SELECT  7, 'CCC', 2019
UNION ALL SELECT  8, 'DDD', 2018
UNION ALL SELECT  9, 'EEE', 2019
UNION ALL SELECT 10, 'FFF', 2019
UNION ALL SELECT 11, 'GGG', 2019
)
-- 2. Recursive SQL 이용
, t1 AS
(
SELECT id
     , MIN(CASE WHEN reg_uyear = 2019 THEN reg_uyear END) reg_uyear
  FROM t
 GROUP BY id
 UNION ALL
SELECT b.id
     , b.reg_uyear
  FROM t1 a
 INNER JOIN t b
    ON a.id = b.id
   AND a.reg_uyear - 1 = b.reg_uyear
)
SELECT id
     , COUNT(reg_uyear) cnt
  FROM t1
 GROUP BY id
;