Se você incluir outras colunas, também precisará incluir uma cláusula GROUP BY
SELECT AnotherColumn, SUM(DATEDIFF(day, StartDate, EndDate)+1) AS myTotal
FROM myTable
WHERE (Reason = '77000005471247')
GROUP BY AnotherColumn
SELECT AnotherColumn, SUM(DATEDIFF(day, StartDate, EndDate)+1) AS myTotal
FROM myTable
WHERE (Reason = '77000005471247')
GROUP BY AnotherColumn