We've been using polycord since 2010, and honestly, no problems. As long as we follow the instructions and cut it 11% shorter than measured, it works beautifully. It doesn't just work for applications like collecting balls; if you want to prevent a motor from stalling, use polycord on a pully designed for a toothed belt, and the polycord will start to slip before the motor stalls. You can change its tension to adjust how much force it takes to make it slip.
The belts on our grabber in 2011 would fall off every once in a while, but that was more a symptom of
the design of the rollers than anything else. It wasn't a problem, either; there were 4 belts on each side, and it only took 1 for the grabber to work. It was also the only part of the robot that worked at all that year, but at least it gave us something to be proud of, dog toys and all!