Hmm happened to me once, was going back from a down-hill and the engine was turned off. I thought it would be easy yeh and kept on going, When I needed to brake, the brake pedal was stiff and the car didn't brake, that freaked me out!
I personally believe(please correct me) that Power-fluid brake cars need the engine running to brake properly.
While running the Vitz on cng, doesn't the engine get under-powered to process the brake fluid through the brakes? Or maybe the brake fluid has decreased/leaked. Check that too, since that's very important=)
Sorry, I am not too much use when it comes to cars, the above is just about experience I had in a Santro.
Hope it gets better:)