I had two of these plastic parts snap on the same drawer at the top of the stairs. I got two replacements and when doing the "fix" noticed that the vertical wood slats they were attached to at the rear were "floating"...not fastened at the bottom because the flimsy staples didn't hold them to the floor. I replaced the fasteners and made sure all the fasteners in the entire drawer system were solid and have had no problems since then. I also looked at all the other drawers in the unit (kitchen, bath, bedroom, etc.) and did whatever was necessary to strengthen those also (nothing at all -
).
IMO, the breakage occurs not because they are plastic, but because they are not installed in a way which limits their movement. When the movement is too severe, they break because they aren't designed for that sort of bending.