My current daily wear corset recently developed this problem. In addition, there is wear from the laces across the back edge of the corset, as you can see. Otherwise the corset is in good shape, so I need to get more wear out of it.
It's actually fairly easy to fix this problem even if you've never made a corset. So long as you have basic sewing skills, you can repair your corset fairly easily.
1. The first step is cutting a strip of material to patch the corset. Mine is imported coutil, which is the original material of the corset and the strongest I can use. I cut my strip 2" wide and the same length or a little longer than the length of the corset.
2. Fold both sides on the strip in to meet in the middle and press.
3. Unpick the stitching on the binding of the corset for about an inch.
4. Cover the back edge of the corset with your folded strip. Position your needle at the edge of the folded strip, making sure to catch the back at the same time. Make sure your strip doesn't hit any of the grommets. Mine hits right on the edge of them.
5. Replace the binding, wrapping it from front to back, tucking all the ends in, and stitch the binding down.
The back edge of your corset is now super-reinforced with two extra layers of fabric. It should add months or more of wear to your corset.
And now I will be doing what I should have done from the beginning and add flossing to the ends of these bones to help prevent this from happening again. It's too bad that I'm horrible at embroidery.