Calculating Running Total After Reset
Here's one method of getting running totals after reset. There are probably others out there. Here is your test data:

CREATE TABLE user20907 (
ID INTEGER NULL,
CUSTOMERID INTEGER NULL,
AMOUNT INTEGER NULL,
RESETYN INTEGER NULL
);

BEGIN TRANSACTION;
INSERT INTO user20907 VALUES (1,111,5,0);
INSERT INTO user20907 VALUES (2,111,6,0);
INSERT INTO user20907 VALUES (3,111,7,1);
INSERT INTO user20907 VALUES (4,111,8,0);
INSERT INTO user20907 VALUES (5,111,9,0);
INSERT INTO user20907 VALUES (6,111,4,1);
INSERT INTO user20907 VALUES (7,111,7,0);
INSERT INTO user20907 VALUES (8,111,9,0);
COMMIT TRANSACTION;


First get a running total of the ResetYN column. I'm going to call it SUM_OF_RESETYN. In an outer query you can partition by both CustomerID and SUM_OF_RESETYN. For the reset running total, instead of taking Amount directly you can do a case statement similar to what you already have:

SELECT
      t.ID
    , CUSTOMERID
    , AMOUNT
    , RESETYN
    , RUNNINGTOTAL
    , SUM(CASE WHEN RESETYN = 1 THEN 0 ELSE AMOUNT END) OVER (PARTITION BY CUSTOMERID, SUM_OF_RESETYN ORDER BY ID) RESETRUNNINGTOTAL
FROM
(
    SELECT
          ID
        , CUSTOMERID
        , AMOUNT
        , RESETYN
        , SUM(AMOUNT) OVER (PARTITION BY CUSTOMERID ORDER BY ID) RUNNINGTOTAL
        , SUM(RESETYN) OVER (PARTITION BY CUSTOMERID ORDER BY ID) SUM_OF_RESETYN
    FROM user20907
) t;


I ran that query and the results matched yours, except that I did not have a NULL value for RESETRUNNINGTOTAL for ID 1. Was that intentional? If so it should be easy to integrate that bit of logic into my query.