Are broken pedals common? Yes.
Your particular pedal? Who knows?
There is a vast ocean of depth regarding quality [durability] when it comes to any bike part. Nylon pedals range from 'literally just nylon, with the body of the pedal acting as a bushing' to 'glass-fiber composite plastics, with sleeve and ball bearings'.
We cannot know what you have without a picture, but even if we did, sometimes stuff breaks. That would be why most manufacturers offer some kind of warranty on parts. "Breaks", by itself, is vague, as well. What broke? A bearing? Axle? Pedal body? Pins?