Unfortunately, using both rewinddir and seekdir didn't help. Instead of getting nothing the second time through the loop, the array was populated with the values of the files that were previously there and now nonexistent. It may have something to do with the fact that I'm running this on a Win32 platform, I dunno.
I just moved the opendir and closedir inside the loop, and it works fine now. It makes me feel dirty to have code that opens and closes a directory handle roughly once a second, but it works for now.