They were just a steel rivet so they decayed and when they oxidized in place they broke...Bet you could get a shoemaker to install a new one, carefully open the thread and change it. Then he can replace the thread, you can darken it with dye so no one can tell. I've done such with some in past. I couldn't stand them being out of sorts.
That one's for the .45, the one for the revolver is different. Easy to distinguish when you see it.