Test your code before posting it!
try:
CREATE TABLE #Test
(
EmployeeID Int,
LogTime DateTime
)
INSERT INTO #Test
select 1001, '01/01/2010 10:22:36'
union select 1002, '01/01/2010 10:24:37'
union select 1003, '01/01/2010 10:24:38'
union select 1001, '01/01/2010 10:24:39'
union select 1001, '01/01/2010 10:24:40'
union select 1002, '01/01/2010 10:24:45'
union select 1003, '01/01/2010 10:26:45'
--drop table #qupd
select EmployeeID, LogTime, cast(Null as datetime) as PrevLogTime, cast(null as int) as TimeDiff
into #qupd
from #Test
create clustered index cix_qupd on #qupd(EmployeeID, LogTime)
declare @PrevLogTime datetime
declare @TimeDiff int
declare @EmployeeId int
update #qupd set
@PrevLogTime = PrevLogTime = CASE WHEN (EmployeeID = @EmployeeId) THEN @PrevLogTime ELSE NULL END
,@TimeDiff = TimeDiff = DATEDIFF(minute, @PrevLogTime, LogTime)
,@EmployeeId = EmployeeID
,@PrevLogTime = LogTime
option (maxdop 1)
select EmployeeID, LogTime
from #qupd
where PrevLogTime is null or TimeDiff > 1
Please note: you have entries in your sample data for EmployeeID 1001 whcih are more than 1 minute appart, so you should expect them to be shown in results.