Putting The Date And Time In A Log Filename

Here's what I want:
I have a DTSX package run as a SQL Server agent job, that each time it runs I want it to create a new log file with the date & time in the filename.
e.g. MyJobLog.20080311_103613.txt

I have implemented this using the SSIS log provider for Text Files, and defining the Connection String as an expression as follows:-




Code Snippet"MyJobLog." + (DT_STR,4,1252)YEAR( DATEADD( "dd", -1, getdate() )) +RIGHT("0" + (DT_STR, 2, 1252) MONTH( GETDATE() ), 2) +RIGHT("0" + (DT_STR, 2, 1252) DAY( GETDATE() ), 2)+ "_" +RIGHT("0" + (DT_STR, 2, 1252) datepart("hh", GETDATE() ) , 2)+RIGHT("0" + (DT_STR, 2, 1252) datepart("mi", GETDATE() ) , 2)+RIGHT("0" + (DT_STR, 2, 1252) datepart("ss", GETDATE() ) , 2)+".txt"






Here's the problem:-
When the job runs, each time it tries to write to the log file it re-evaluates the filename, and as the seconds pass by the name changes! So instead of one file I end up with several:-
e.g.
MyJobLog.20080311_103613.txt
MyJobLog.20080311_103614.txt
MyJobLog.20080311_103615.txt


So the one execution of the job is now divided across three files! This is not what want!

Here's one way I fixed it:-
One of my Jobs is run from an MS-DOS batch file, so I was able to pass the constructed date/time sting into the DTSX file as a parameter. This works perfectly.

Here's my problem:-
Three more of my jobs are run as scheduled job from SQL Server Agent, so I can't pass in the date/time as a parameter each time (unless you know otherwise). And the clients' security policy won't allow the job to call an MS-DOS batch file which runs the DTSX package.
Or is there really some other way to stop the Log filename from re-evaluating on every write?