Leather belts. Same problem as elastic, probably exactly the same, with degradation of elastin. They fail, and I am not confident I can tell by looking how long a used belt is going to last. Plus, all the used belts I see at thrifts in my area are clearly already worn out to the point that there would be no purpose to having them at all. I do buy belts new, online, but top out at about US $35.
I've never experienced this, even with my oldest belts. It occurred to me that in order to stretch, you may be wearing them too tight,....but then, why not just tighten by one hole once you find them loose? Or buy a thicker belt less prone to stretching?