Found this thread looking for a solution to my problem. Mine required a different solution that I figured out that might be of use to others. My macro was deleting rows, shifting up, and copying rows to another worksheet. Memory usage was exploding to several gigs and causing "out of memory" after processing around only 4000 records. What solved it for me?
application.screenupdating = false
Added that at the beginning of my code (be sure to make it true again, at the end) I knew that would make it run faster, which it did.. but had no idea about the memory thing.
After making this small change the memory usage didn't exceed 135 mb. Why did that work? No idea really. But it's worth a shot and might apply to you.