>Since I'm closing each file after I open it, what limit could that be?

I've had similar trouble when I tried to use Word with hundreds of files, and it choked at about 200. Watch your memory consumption go up as each file is processed. Office apps build internal lists so every file you open adds to them. I've seen the memory used go up in increments of, IIRC, 36K for each file, and no matter that each file was immediately closed, the memory was never released, until the moment I had to invoke task manager and euthanise the critter.

So find your measure, how many files can it do before it chokes, and then kill it gracefully when it reaches about half that mark, just to stay on the safer side (as I don't believe there's a side which is exactly safe in Office automation).