SQL "With As" Alternative Way

In a previous question, you guys helped me grab data from a different row. The statement I am using works perfectly on the MS SQL Server Managment Studio. I can run the statement without any errors and I return the data I need. However, I need to run this data on our frontend program. When I try to run my statement on this program, it just hangs. I have a feeling that the "With As" part of this statement is causing problems. Is there anyway to rewrite this statement by putting this temporary table in a subquery?

WITH Temp1 AS (SELECT
SkillTargetID = Agent_Logout.SkillTargetID,
LogoutDateTime = Agent_Logout.LogoutDateTime,
LogonDate = DateAdd(s,-1 * Agent_Logout.LoginDuration,Agent_Logout.LogoutDateTime),
ROW_NUMBER() OVER(PARTITION BY Agent_Logout.SkillTargetID ORDER BY Agent_Logout.LogoutDateTime ASC) RowVersion,
LoginDuration = Agent_Logout.LoginDuration
FROM Agent_Logout)

SELECT
AgentID = Base.SkillTargetID,
LogonDate = Base.LogonDate,
BaseLogout = Base.LogoutDateTime,
BaseDuration = Base.LoginDuration,
NextLogon = Temp1.LogonDate,
LogoutDuration = DateDiff(s,Base.LogoutDateTime,Temp1.LogonDate)
FROM Temp1 Base
LEFT JOIN Temp1 ON Base.SkillTargetID = Temp1.SkillTargetID
AND Base.RowVersion = Temp1.RowVersion-1

Solution

Below is what I ended up with. This works with the Cisco front-end program we use.

DECLARE @dtStartDateTime DATETIME, @dtEndDateTime DATETIME, @agentid VARCHAR
SET @dtStartDateTime = :start_date SET @dtEndDateTime = :end_date
SELECT
    FullName = Temp1.FullName,
    AgentID = Temp1.SkillTargetID,
    LogonDate = Temp1.LogonDate,
    LogoutDate = Temp1.LogoutDateTime,
    LoginDuration = Temp1.LoginDuration,
    RowVersion# = Temp1.RowVersion,
    AgentID2 = Temp2.SkillTargetID,
    LogonDate2 = Temp2.LogonDate,
    LogoutDate2 = Temp2.LogoutDateTime,
    RowVersion#2 = Temp2.RowVersion,
    LogoutDuration = DateDiff(s,Temp1.LogoutDateTime,Temp2.LogonDate)

FROM

(SELECT
    FullName = Person.LastName + ', ' + Person.FirstName,
    SkillTargetID = Agent_Logout.SkillTargetID,
    LogoutDateTime = Agent_Logout.LogoutDateTime,
    LogonDate = DateAdd(s,-1 * Agent_Logout.LoginDuration,Agent_Logout.LogoutDateTime),
    ROW_NUMBER() OVER(PARTITION BY Agent_Logout.SkillTargetID ORDER BY Agent_Logout.LogoutDateTime ASC) as RowVersion,
    LoginDuration = Agent_Logout.LoginDuration
    FROM Agent_Logout, Agent, Person
    WHERE Agent_Logout.SkillTargetID = Agent.SkillTargetID and Agent.PersonID = Person.PersonID
) Temp1,

(SELECT
    SkillTargetID = Agent_Logout.SkillTargetID,
    LogoutDateTime = Agent_Logout.LogoutDateTime,
    LogonDate = DateAdd(s,-1 * Agent_Logout.LoginDuration,Agent_Logout.LogoutDateTime),
    ROW_NUMBER() OVER(PARTITION BY Agent_Logout.SkillTargetID ORDER BY Agent_Logout.LogoutDateTime ASC) as RowVersion
    FROM Agent_Logout
    WHERE Agent_Logout.SkillTargetID = Agent_Logout.SkillTargetID
) Temp2

WHERE Temp1.SkillTargetID = Temp2.SkillTargetID and Temp1.RowVersion = (Temp2.RowVersion - 1) AND
(Temp1.LogonDate >= :start_date 
And Temp1.LogonDate <= :end_date) AND
Temp1.SkillTargetID IN (:agentid)
ORDER BY Temp1.SkillTargetID, Temp1.RowVersion