I RARELY play my DS these days. I had an original version (that I got in exchange for pulling a 24 hour shift in the army) and it lasted through two deployments and all the mistreatment one can imagine resulting from such (minus the explosions apparently). A few years back I replaced the aging system with a DS lite and donated my old one to my mother who actually plays it regularly. After a few dozen uses in it's entire life, the hinge snapped.
In retrospect, the reason this seems to be common lies in the hinge itself. The ds lite hinge has a much shorter halting point than the original. Even with similar materials and tolerances, it remains likely that general use, frequently running against this hard stop, would result in material fatigue and eventual breaking. Aside from that simple logic, the fact the hinge that broke was on the right side of the device coupled with the fact that I generally hold the device in my left hand and open it with my right, seems to support this assumption.