After three umbrellas I got to thinking there has to be a better way and being a hands-on guy I think I've come up with a reasonable fix. I've seen web pages suggesting a fiberglass rod to replace the supporting rod. That's pretty good. They are flexible and chances are if it falls again it would flex enough but another rod would break or bent. I don't have small fiberglass rods like that and they could be hard to find. Like other folks I want to do something with materials on-hand or something I could get my hands on quickly.
If you looks at the supporting rods they are actually long skinny strips of metal bent in a “U” shape along the length of the rod. Instead of using a solid cylinder style rod they use a “U” shape rod for cost and ease of assembly. Instead of replacing the rod I'm thinking of reinforcing the rods. So my answer is wired coat hangers.