I have never encountered this particular error myself; however if I may toss in a couple of thoughts:
1. Is there an increased load being placed on the server of late?
2. Are there a number of DTS tasks scheduled to run simultaneously?
3. Are there other OS or application tasks scheduled to run at or near the same time as this package?
4. Do you know precisely what step DTS is failing on?
5. Is it possible to schedule and run this task from another SQL Server?
Some additional thoughts (which you may already know and I apologize if you do):
1. DTS runs in a separate memory space from SQL Server; multiple DTS packages running simultaneously will degrade the amount of RAM available.
2. There is a windows registry setting for throttling the number of DTS (or was it command -- .exe -- objects that can run simultaneously). I think the default is 10. Search MSDN.
3. If you use DTS heavily on one server, consider throttling back the amount of memory available to SQL Server; I know that this is NOT recommended by MS, but I have done this in the past with a good deal of success.
I hope that you can trace the roots of your issue; good luck.
Have you hugged your backup today?