Adding a 'last time occurred' flag column
This cannot be done with a computed column. One option is to use a trigger:

Sample data

CREATE TABLE dbo.Example
(
    GroupKey integer NOT NULL,
    [Status] integer NOT NULL,
    inserted_date datetime NOT NULL DEFAULT GETUTCDATE(),
    IsLastTimeOccurred bit NOT NULL DEFAULT 'false',

    CONSTRAINT PK_dbo_Example_GroupKey_Status_inserted_date
    PRIMARY KEY CLUSTERED (GroupKey, [Status], inserted_date)
);

INSERT dbo.Example
    (GroupKey, [Status], inserted_date)
VALUES
    (11136, 10, '2015-03-30T13:01:50.153'),
    (11136, 11, '2015-03-30T13:02:03.590'),
    (11136, 12, '2015-03-30T13:02:08.980'),
    (11136, 10, '2015-04-30T09:37:40.477'),
    (11136, 11, '2015-04-30T09:37:46.400'),
    (11136, 12, '2015-04-30T09:38:04.177');


Initial setting

This assumes the rows all have IsLastTimeOccurred = false to begin with:

UPDATE E
SET IsLastTimeOccurred = 'true'
FROM dbo.Example AS E
WHERE NOT EXISTS
(
    SELECT * 
    FROM dbo.Example AS E2
    WHERE E2.GroupKey = E.GroupKey
    AND E2.[Status] = E.[Status]
    AND E2.inserted_date &gt; E.inserted_date
);


Maintenance

The following trigger ensures the column stays correct when the table changes:

CREATE TRIGGER trg_dbo_Example_AIUD
ON dbo.Example
AFTER INSERT, UPDATE, DELETE
AS
BEGIN
    SET ROWCOUNT 0;
    SET NOCOUNT ON;

    SET TRANSACTION ISOLATION LEVEL SERIALIZABLE;

    -- Holds group keys and the latest insert date
    CREATE TABLE #Changes
    (
        GroupKey integer NOT NULL,
        [Status] integer NOT NULL,
        inserted_date datetime NOT NULL,

        PRIMARY KEY (GroupKey, [Status])
    );

    -- Populate the temporary table    
    INSERT #Changes
    (
        GroupKey, 
        [Status],
        inserted_date
    )
    SELECT
        E.GroupKey, 
        E.[Status],
        MAX(E.inserted_date)
    FROM dbo.Example AS E
    WHERE EXISTS
    (
        SELECT * 
        FROM Inserted AS I
        WHERE I.GroupKey = E.GroupKey
        AND I.[Status] = E.[Status]

        UNION ALL

        SELECT * 
        FROM Deleted AS D
        WHERE D.GroupKey = E.GroupKey
        AND D.[Status] = E.[Status]        
    )
    GROUP BY
        E.GroupKey,
        E.[Status];

    -- Set the flag
    UPDATE E
    SET E.IsLastTimeOccurred =
        CASE WHEN E.inserted_date = C.inserted_date THEN 1 ELSE 0 END
    FROM #Changes AS C
    JOIN dbo.Example AS E
        ON E.GroupKey = C.GroupKey
        AND E.[Status] = C.[Status]
    WHERE
        E.inserted_date = C.inserted_date
        OR E.IsLastTimeOccurred = 'true';
END;


This is a general solution that handles inserts, updates, and deletes. It was written before the question was clarified to state that the table was insert-only. Even so, I would probably leave the full general logic in; it doesn't cost much, and provides a safety net.