There's a feed linkage that gets frozen up. I had one old Kenmore that wouldn't let go for anything. I finally had to use Dawn dishsoap on a Q-tip. That stuff really breaks up the old grease. LOL! Hopefully, your won't come to that.
If you look in the bottom of the machine, and follow what's supposed to move when you push the back-stitch button, you'll discover the culprit. On some, it's a plastic tube with a plunger. On other's it's the feed dog drop linkage, right in the front of the machine, just right of the hook. It has a little metal barrel that won't turn. It needs oil on the shaft and grease on the outside flat surface.