From a Tech Support standpoint when my users complain that any application is suddenly slowed down, the first thing I do is delete all of the tmp files on the machine. When it comes to Excel, their complaint is generally that EVERY Excel file opens and responds slowly. Even though you indicated that you're running a subroutine and experiencing this in a particular workbook, it still may be worth it to delete all of the .tmp files from the machine. I've seen on at least 5 seperate occasions where the .tmp's had brought Excel to a crawl and once I deleted those, the problem cleared up immediately.
Assumimg it's not related to your code, it could also be memory related in the sense that after the routine runs for so long, it begins accessing an area of RAM that's bad (I've had this happen with other software.) Likewise, do you have enough memory
To rule memory out, run the subroutine on a different PC if possible. Although I seriously doubt it's memory related, it may be worth trying unless you're convinced that it's somewhere in your code

Tony