This should give you more accurate totals, although it will list every combination of ProductionLine and Category, which may not be what you want.

SELECT D.Line AS Line, D.ProductionLine AS ProductionLine, D.Shift AS Shift, D.DownTime,

R.Category, R.AssignedDowntime,

CONVERT(VARCHAR(10), D.DatePacked,101) AS DatePacked

FROM (

SELECT Line, Shift, DatePacked, Category,

SUM(Cast(R.Downtime AS INT)) AS AssignedDowntime

FROM Production.DownTimeReason

WHERE (DatePacked >= '20150127'

AND DatePacked < '20150128')

GROUP BY Line, Shift, DatePacked, Category

) AS R

LEFT OUTER JOIN (

SELECT Line, Shift, DatePacked, ProductionLine,

SUM(CAST(D.DownTime AS INT)) AS DownTime

FROM Production.DownTimeHistory

WHERE (DatePacked >= '20150127'

AND DatePacked < '20150128'

AND DownTime != 0

AND Shift = '1')

GROUP BY Line, Shift, DatePacked, ProductionLine

) AS D

ON D.Line = R.Line

AND D.Shift = R.Shift

AND D.DatePacked = R.DatePacked

ORDER BY D.Line, D.Shift, D.DatePacked