My zx12r cuts out while riding them wont start

Sounds to me like you have a stuck float in the carburetor. It's only allowing a trickle of gas from the tank into the bowl. When the gas is used up, it dies. It won't start right away because it's out of gas. It takes some time before there is enough gas in the bowl for it to start. I'm guessing that if you let it sit for longer, it takes a little longer to die? If you can remove the carb, do so. Flip it over and let the gas drain into something. See those four screws? Take them out. Now it's time you understand the carb and how it works. You will see the float, it's the biggest moving part in the carb. It should be hinged to the body by a little pin.if you move it up and down, you will see that it moves a little piston that goes into the fuel port. Try not to bend the place where it attaches as this is how you adjust the fuel level in the bowl, and may end up having gas pour out till your tank is empty! If you push the pin out the float will come off. Now the piston is sharp on one end. That end goes up into the carb, and when the float pushes hard enough on it, stops fuel from entering the bowl. If all the parts are moving freely, spray with some carb cleaner and re assemble. You can check the flow by putting a hose on the fuel inlet ( the spot where the tank hooks to the carb) and blowing through it while moving the float up and down. You should be able to pass air until the float reaches the top of its travel. If not, it will need to be adjusted by slightly bending those little tabs where the piston attaches to the float. A little trial and error, and you should have your bike up and running again. Hope this helps!

You should measure the fuel pump's supply first to check that the pump works ok.
When it dies, do you hear the pump pressing your ear against the fuel tank and turning the key to on position and your kill switch to on too?You should hear it working for 3 sec.If not working at all start by checking the pump's relay and then the pump itself.