[Al Skierkiewicz]

Ryan,
I think you can see from the above posts that there are variety of reasons for these robots being able to push and not trip breakers. This is some of what I have observed over the past few years working from the electrical side... Teams that are able to push will never have large tires (4-6" seem to be the average). Custom gearboxes or special transmissions are used. The software is written so that the motors are not driven at max input power or software backs down after a predetermined period of sustained pushing. The tires are not extremely sticky so that under extreme pushing the tires slip. Or my personal favorite, the drivers are so well practiced that they know their machines and don't push them to the limit.
No teams that are able to last a prolonged pushing session would be able to last through a four minute match or longer. All of the variables (heat, voltage, friction, breaker temperature) will combine to trip breakers, reset the controller or set off the main.