Stock tires? If so, I think that's your problem. I've had endless troubles with Continentals and blowouts in the past...even when pumped up to the nominal pressure. You may want to reduce the pressure by about 10% which has worked in the past for me.

That said, you may also want to assess your riding style. I ride aggressively as well but even if I go off a curb or go up a curb, I do as much as possible to reduce the load on the wheels before impact. I don't know much about your riding style but if you are just slamming the wheel into the curb or just dropping it off the curb, that can put a lot of force on the tire.

Try lifting the front wheel up the curb (push down on the tire first then rock back to pop the wheel into the air) and then rocking forward and lifting the rear wheel with your feet on the pedals. It's easier to do if you have clipless but if you have platforms, you can still lift the rear wheel by rotating your wrists forward and moving your center of gravity forward at the same time.

When you go down a curb, rock back as the front wheel goes off and then rock forward as rear wheel goes off. This takes a lot of force on the wheels.

As for tires, I've had very good luck with Vittoria tires. The Voyager Hyper is a very nice tire for urban riding. Be aware that it runs much bigger than the size they list. A "35" mm tire is actually 37mm wide. It even says that on the casing.