The original cotton string was starting to wear down. It broke once already, but it was just the very end that snapped off, so I could just tie a new knot and call that the new end. But now it was starting to do it again. I bought some paracord from the hardware store and replaced it with that.

Right after I pulled the original string out of the waistband, I remembered that someone once told me that you can tie the new string to the old string, and then pull the old string out and thereby pull the new string into the hole, instead of trying to push the new string through the hole. That would have been a good thing to have remembered about 30 seconds earlier.