We’ve never had a drawstring break itself, but it’s common for the “spools” (“bobbins”) at the frame bottoms to break. The installers didn’t always take a wrap around the spool shaft to take the stress, and the knotted string end would crack and break through the hole in the spool flange.
If your string broke instead from wear, and you can’t knot in a short length of cord to make up for the single repair knot’s resulting length loss, it’s likely the only fix is a new string.
Joel