Remove the s.StateDuration from the GROUP BY. You're SUMMING that... Your query should look like this:
SELECT s.AgentName
  , s.ReasonCode
  , Sum(s.StateDuration) AS 'StateDuration'
FROM (
  SELECT [Agent Name] AS 'AgentName'
   , [Reason Code] AS 'ReasonCode'
   , Cast(Datepart(Second, [Duration]) AS INT) + Cast(60 * Datepart(Minute, [Duration]) AS INT) + Cast(3600 * Datepart(Hour, [Duration]) AS INT) AS 'StateDuration'
  FROM State_Details
  GROUP BY [Agent Name]
   , [Reason Code]
  ) s
GROUP BY s.AgentName
  , s.ReasonCode