Remove set XACT_ABORT ON and implement TRY CATCH http://msdn.microsoft.com/en-us/library/ms175976%28v=sql.100%29.aspx, so this proc should looks like (I can't test it so first test it):

CREATE PROCEDURE [dbo].[proc_Master_Schedule]

AS

-- set XACT_ABORT ON --line to remove

DECLARE @Count INT

DECLARE@LoopCount INT

DECLARE@ProgramID INT

DECLARE @strMessage NVARCHAR(MAX)

DECLARE @subject NVARCHAR(MAX)

SELECT IDENTITY(INT,1,1) ID, [ProgramID] INTO #tmpProgram

FROM dbo.Schedule_Setup WITH (NOLOCK)

WHEREDeleted=0

SELECT @Count = @@RowCount

SET @LoopCount = 1

WHILE @LoopCount <= @Count

BEGIN

SELECT @ProgramID=ProgramID

FROM #tmpProgram

WHERE ID = @LoopCount

--TRY CATCH block

BEGIN TRY

EXEC dbo.proc_Schedules @ProgramID

END TRY

BEGIN CATCH

SET @Message = 'The Schedule for Program ' + CONVERT(NVARCHAR,@ProgramID) + 'failed.'

exec Master.dbo.sp_sendSAM

@recipients='Dev.Team@test.com',

@subject='proc_Master_Schedule failure',

@sender_email = 'SQL2008@test.com',

@Message = @Message,

@format ='html'

END CATCH;

--end of TRY CATCH block

SET @LoopCount=@LoopCount + 1

END

DROP TABLE #tmpProgram