Using Alan.B's set up data, here's another way (except using DATE data type):

-- Setup

IF OBJECT_ID('tempdb..#x') IS NOT NULL

DROP TABLE #x;

CREATE TABLE #x

( Studentid int, DateID DATE unique, attendaceind bit)

INSERT INTO #x

SELECT 1234, '20121031', 1 UNION ALL

SELECT 1234, '20121102', 1 UNION ALL

SELECT 1234, '20121101', 1 UNION ALL

SELECT 1234, '20121105', 0 UNION ALL

SELECT 1234, '20121107', 1 UNION ALL

SELECT 1234, '20121108', 1 UNION ALL

SELECT 1234, '20121109', 0 UNION ALL

SELECT 1234, '20121113', 0 UNION ALL

SELECT 1234, '20121115', 0 UNION ALL

SELECT 1234, '20121114', 0 UNION ALL

SELECT 1234, '20121116', 0 UNION ALL

SELECT 1234, '20121119', 0 UNION ALL

SELECT 1234, '20121120', 0 UNION ALL

SELECT 1234, '20121126', 0 UNION ALL

SELECT 1234, '20121127', 0 UNION ALL

SELECT 1234, '20121128', 0 UNION ALL

SELECT 1234, '20121129', 0 UNION ALL

SELECT 1234, '20121130', 0 UNION ALL

SELECT 1234, '20121203', 0 UNION ALL

SELECT 1234, '20121204', 0 UNION ALL

SELECT 1234, '20121205', 0 UNION ALL

SELECT 1234, '20121206', 0 UNION ALL

SELECT 1234, '20121207', 0 UNION ALL

SELECT 1234, '20121210', 0 UNION ALL

SELECT 1234, '20121211', 0 UNION ALL

SELECT 1234, '20121212', 0 UNION ALL

SELECT 1234, '20121213', 0 UNION ALL

SELECT 1234, '20121214', 1 UNION ALL

SELECT 1234, '20121217', 1 UNION ALL

SELECT 1234, '20121218', 1 UNION ALL

SELECT 1234, '20121219', 1

GO

DECLARE @startdate DATE='20121114',

@endDate DATE='20121213';

--;WITH Absences AS (

SELECT StudentID, StartDT=MIN(DateID), EndDT=MAX(DateID)

,Absences=COUNT(1-attendaceind)

FROM (

SELECT StudentID, DateID, attendaceind

,n=DATEDIFF(day, DateID

,ROW_NUMBER() OVER (PARTITION BY StudentID ORDER BY DateID))

FROM #x

WHERE attendaceind = 0) a

GROUP BY StudentID, n

-- )

--SELECT StudentID, StartDT=MIN(StartDT), EndDT=MAX(EndDT)

-- ,Absences=SUM(Absences)

--FROM (

-- SELECT StudentID, StartDT, EndDT

-- ,Absences=CASE WHEN StartDT >= @startdate AND EndDT <= @enddate THEN Absences

-- WHEN StartDT < @startdate AND EndDT <= @enddate

-- THEN DATEDIFF(day, @startdate, EndDT)

-- WHEN StartDT >= @startdate AND EndDT > @enddate

-- THEN DATEDIFF(day, StartDT, @enddate)

-- ELSE DATEDIFF(day, @startdate, @enddate) END

-- FROM Absences

-- WHERE EndDT >= @startdate AND StartDT <= @enddate) a

--GROUP BY StudentID

DROP TABLE #x

The initial code provided groups consecutive absences. If you uncomment the rest of the code it then groups again within the provided start and end dates summing up the absences that occur as part of a consecutive group of absences.

When you run the first set of code, notice how one record starts at 11-13? The start date range of 11-14 requires the absence count to be adjusted in the final grouping and that is done with the CASE statement.

All that's left is to add a HAVING clause to filter out only records appearing that are greater whatever your threshold is.

I'm not sure which of the provided solutions will work best for you but surely there's something here you can work with.