sql querying for a pattern
One way of doing it would be to use LEAD.

WITH T AS
(
SELECT  StudentID,
        GradeIssued AS g1, 
        LEAD(GradeIssued, 1) OVER (PARTITION BY StudentID ORDER BY WhenIssued) AS g2,
        LEAD(GradeIssued, 2) OVER (PARTITION BY StudentID ORDER BY WhenIssued) AS g3,
        LEAD(GradeIssued, 3) OVER (PARTITION BY StudentID ORDER BY WhenIssued) AS g4
FROM StudentGrades
)
SELECT DISTINCT StudentID
FROM   T
WHERE  g1 = 'D'
       AND g2 = 'C'
       AND g3 = 'C'
       AND g4 = 'A' 


Another way would be to use XML PATH to concatenate all grades in order and LIKE.

WITH sg1 AS
(
SELECT DISTINCT StudentID
FROM StudentGrades
)
SELECT *
FROM sg1
CROSS APPLY
(
    SELECT GradeIssued + ''
    FROM StudentGrades sg2
    WHERE sg2.StudentID = sg1.StudentID
    ORDER BY WhenIssued
    FOR XML PATH('')
) CA(grades)
WHERE grades LIKE '%DCCA%'