ZX12 fuel starving

Hi my 2000 ZX12 has developed a problem when the fuel level get down to the last 5 to 7 litres and you power on it dies as if starving for fuel hold a steady throttle and it will keep going but as soon as you throttle up id starves any ideas?? Have replaced fuel pump and filter no improvement but fill it up and game on ???

Tank cap breather? My ZRX stopped on the highway on Sunday with low fuel- pulled the tank off and no fuel flow on prime like it should. Pulled tap apart and found nothing wrong with it. Pulled cap apart today and all sorts of shit were in the breather orifices and such. Hopefully this will fix this problem. Not sure if the same could affect an injected bike, but maybe there is a tank breather kinked also? My ZRX is an 08 model, so you'd think that isn't much time for crap to collect in the cap. Your bike is a lot older- more likely I'd guess.