The reason they break is because the fit isn't perfect. Any stresses develop into cracks.....You can take some of the stress out of the mudguard by using rubber washers and nylok nuts.
First, the following is just a hypothesis that does not contradict prevoious comments. So, in short, I could just say, "Like Andrew said." For my own amusement, the hypothesis:
Looking at this from the resonance angle, what Andrew says makes perfect sense (of course). Resonance and other vibrations have their work already started in materials under stress. In addition to relieving the stress, rubber washers damp the vibration (obvious, maaybe). I went looking at OldVet's previous posts to learn he has an RGS mudguard on a '62 Super Rocket. Not an RGS expert (or any, maybe), reviewed the mudguard design for what I think can be unexpected sources of resonance. I see that the long, and somewhat spindly, front and rear stays are nearly identical in shape and symetrical in front/rear deployment. This symmetry can, I believe, contribute to resonance. In this case, the reonance would focus on the center-stay connection point. What to do about this? To start, back to "Like Andrew said." Otherwise, perhaps some modificaton or strengthening of either the front or rear stay would help. Problem is, hard to run a test, because the relief of stress at the center stay must come first and that confuses test results.
Thanks for letting me exercise my inner acoustician.
Richard L.